R¹ denotes a C_1-3-alkyl group substituted by a group R_a, where

R_a denotes a 3,4-dihydro-quinolinyl, 3,4-dihydro-isoquinolinyl, 1,4-dihydro-quinazolinyl, 3,4-dihydro-quinazolinyl, 1H-benzo[d][1,2]oxazinyl, 4H-benzo[e][1,3]oxazinyl, 4H-benzo[d][1,3]oxazinyl or 2H-benzo[1,4]oxazinyl group, wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and in the heterocyclyl moiety a methylene group may be replaced by a carbonyl group,

a 4H-benzo[e][1,3]thiazinyl, 4H-benzo[d][1,3]thiazinyl or 2H-benzo[1,4]thiazinyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and in the heterocyclyl moiety a methylene group may be replaced by a carbonyl group and the sulphur atom may be replaced by a sulphinyl or sulphonyl group,

a 2-oxo-2H-benzo[e][1,3]oxazinyl or 2,2-dioxo-1H-benzo[c][1,2]thiazinyl group wherein in each case in the benzo moiety

one to three methyne groups may each be replaced by a nitrogen atom,

a 2,3-dihydro-1H-benzo[e][1,4]diazepinyl, 4,5-dihydro-3H-benzo[b][1,4]diazepinyl or 5-oxo-4,5-dihydro-3H-benzo[e][1,4]diazepinyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and in the heterocyclyl moiety a methylene group may be replaced by a carbonyl group,

a 2,3-dihydro-benzo[f][1,4]oxazepinyl or 2,3-dihydro-benzo[b][1,4]oxazepinyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and in the heterocyclyl moiety a methylene group may be replaced by a carbonyl group,

a 2,3-dihydro-benzo[b][1,4]thiazepinyl or 2,3-dihydro-benzo[f][1,4]thiazepinyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and in the heterocyclyl moiety a methylene group may be replaced by a carbonyl group and the sulphur atom may be replaced by a sulphinyl or sulphonyl group,

a 5-oxo-4,5-dihydro-benzo[f][1,3,4]oxadiazepinyl group wherein

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom,

a 11H-dibenzo[b,e]azepinyl or 5H-dibenzo[a,d]cycloheptenyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and the methylene group in the heterocyclyl moiety may be replaced by an oxygen or sulphur atom, a carbonyl, sulphinyl or sulphonyl group or by an imino group substituted by R_x, where

R_x denotes a hydrogen atom or a C_1-4-alkyl, C_2-4-alkenyl, C_2-4-alkynyl, C_3-6-cycloalkyl, C_3-6-cycloalkyl-C_1-3-alkyl, aryl, aryl-C_1-3-alkyl, hydroxy-C_2-4-alkyl, C_1-3-alkyloxy-C_2-4-alkyl, C_3-6-cycloalkyloxy-C_2-4-alkyl, amino-C_2-4-alkyl, C_1-3-alkylamino-C_2-4-alkyl, di-(C_1-3-alkyl)-amino-C_2-4-alkyl, C_1-3-alkyl-carbonyl, C_1-3-alkyloxy-carbonyl, C_1-3-alkyloxy-carbonyl-C_1-3-alkyl, aryl-carbonyl, C_1-3-alkyl-sulphonyl or aryl-sulphonyl group,

a phenanthridinyl group wherein

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom, and

a 1,2,3,4-tetrahydro-phenanthridinyl, 1,2,3,4,4a, 10b-hexahydro-phenanthridinyl, 2,3-dihydro-1H-4-aza-cyclopenta[a]naphthyl or a 8,9,10,11-tetrahydro-7H-6-aza-cyclohepta[a]naphthyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom and one or two methylene groups may each be replaced by an oxygen atom or a carbonyl group, while, if two methylene groups are each replaced by an oxygen atom, the oxygen atoms must be separated from one another by at least two methylene units,

a phenanthrenyl group wherein

in each case one to three of the methyne groups in position 1 to 4 and 5 to 8 may each be replaced by a nitrogen atom,

a 1,2,3,4-tetrahydro-phenanthrenyl or a 1,2,3,4,5,6,7,8-octahydro-phenanthrenyl group wherein

in each case one or two of the methylene groups in position 1 to 4 and 5 to 8 may each be replaced by an oxygen atom or a carbonyl group, while, if two methylene groups are each replaced by an oxygen atom, the oxygen atoms must be separated from one another by at least two methylene units,

a 5H-benzo[e]pyrrolo[1,2-a][1,4]diazepinyl, thieno[3,2-b][1,4]benzoxazepinyl, 5H-dibenzo[d,f][1,3]diazepinyl or a 5-oxa 7-aza-dibenzo[a,c]cycloheptenyl group wherein in each case

in the benzo moiety one to three methyne groups may each be replaced by a nitrogen atom,

a naphtho[1,2-d]oxazolyl, naphtho[2,1-d]oxazolyl , naphtho[1,2-d]thiazolyl, naphtho[2,1-d]thiazolyl, naphtho[1,2-d]imidazolyl, naphtho[1,2-b]furanyl or naphtho[2,1-b]furanyl group wherein in each case

in the naphthyl moiety one to three methyne groups may each be replaced by a nitrogen atom,

or a furo[3,2-c]isoquinolinyl, pyrazolo[1,5-c]quinazolinyl or 1H-perimidinyl group,

while the methylene and methyne groups of the above mentioned groups R_a may be substituted by the groups R¹⁰, R¹¹, R¹² or R¹³ and additionally by a C_1-3-alkyl group and the imino groups of the above mentioned groups R_a may be substituted by the groups R_x as hereinbefore defined and

R¹⁰ denotes a hydrogen atom,

a fluorine, chlorine, bromine or iodine atom,

a C_1-4-alkyl, hydroxy, or C_1-4-alkyloxy group,

a nitro, amino, C_1-3-alkylamino, di-(C_1-3-alkyl)amino, cyano-C_1-3-alkylamino, N-(cyano-C_1-3-alkyl)-N—(C_1-3-alkyl)-amino, C_1-3-alkyloxy-carbonyl-C_1-3-alkylamino, pyrrolidin-1-yl, piperidin-1-yl, morpholin-4-yl, piperazin-1-yl, or 4-(C_1-3-alkyl)-piperazin-1-yl group,

a C_1-3-alkyl-carbonylamino, arylcarbonylamino, aryl-C_1-3-alkyl-carbonylamino, C_1-3-alkyloxy-carbonylamino, aminocarbonylamino, C_1-3-alkylaminocarbonylamino, di-(C_1-3-alkyl)aminocarbonylamino, pyrrolidin-1-yl-carbonylamino, piperidin-1-yl-carbonylamino, morpholin-4-yl-carbonylamino, piperazin-1-yl-carbonylamino or 4-(C_1-3-alkyl)-piperazin-1-yl-carbonylamino, C_1-3-alkyl-sulphonylamino, bis-(C_1-3-alkylsulphonyl)-amino, aminosulphonylamino, C_1-3-alkylamino-sulphonylamino, di-(C_1-3-alkyl)amino-sulphonylamino, pyrrolidin-1-yl-sulphonylamino, piperidin-1-yl-sulphonylamino, morpholin-4-yl-sulphonylamino, piperazin-1-yl-sulphonylamino or 4-(C_1-3-alkyl)-piperazin-1-yl-sulphonylamino, (C_1-3-alkylamino)thiocarbonylamino, (C_1-3-alkyloxy-carbonylamino)carbonylamino, arylsulphonylamino or aryl-C_1-3-alkyl-sulphonylamino group,

an N—(C_1-3-alkyl)-C_1-3-alkyl-carbonylamino, N—(C_1-3-alkyl)-arylcarbonylamino, N—(C_1-3-alkyl)-aryl-C_1-3-alkyl-carbonylamino, N—(C_1-3-alkyl)-C_1-3-alkyloxy-carbonylamino, N-(aminocarbonyl)-C_1-3-alkylamino, N—(C_1-3-alkyl-aminocarbonyl)-C_1-3-alkylamino , N-[di-(C_1-3-alkyl)aminocarbonyl]-C_1-3-alkylamino, N—(C_1-3-alkyl)-C_1-3-alkyl-sulphonylamino, N—(C_1-3-alkyl)-arylsulphonylamino, or N—(C_1-3-alkyl)-aryl-C_1-3-alkyl-sulphonylamino group,

a 2-oxo-imidazolidin-1-yl, 2,4-dioxo-imidazolidin-1-yl, 2,5-dioxo-imidazolidin-1-yl or 2-oxo-hexahydropyrimidin-1-yl group wherein the nitrogen atom in the 3 position may be substituted in each case by a methyl or ethyl group,

a cyano, carboxy, C_1-3-alkyloxy-carbonyl, aminocarbonyl, C_1-3-alkyl-aminocarbonyl, di-(C_1-3-alkyl)-aminocarbonyl, pyrrolidin-1-yl-carbonyl, piperidin-1-yl-carbonyl, morpholin-4-yl-carbonyl, piperazin-1-yl-carbonyl or 4-(C_1-3-alkyl)-piperazin-1-yl-carbonyl group,

a C_1-3-alkyl-carbonyl or an arylcarbonyl group,

a carboxy-C_1-3-alkyl, C_1-3-alkyloxy-carbonyl-C_1-3-alkyl, cyano-C_1-3-alkyl, aminocarbonyl-C_1-3-alkyl, C_1-3-alkyl-aminocarbonyl-C_1-3-alkyl, di-(C_1-3-alkyl)-aminocarbonyl-C_1-3-alkyl, pyrrolidin-1-yl-carbonyl-C_1-3-alkyl, piperidin-1-yl-carbonyl-C_1-3-alkyl, morpholin-4-yl-carbonyl-C_1-3-alkyl, piperazin-1-yl-carbonyl-C_1-3-alkyl or 4-(C_1-3-alkyl)-piperazin-1-yl-carbonyl-C_1-3-alkyl group,

a carboxy-C_1-3-alkyloxy, C_1-3-alkyloxy-carbonyl-C_1-3-alkyloxy, cyano-_1-3-alkyloxy, aminocarbonyl-C_1-3-alkyloxy, C_1-3-alkyl-aminocarbonyl-C_1-3-alkyloxy, di-(C_1-3-alkyl)-aminocarbonyl-C_1-3-alkyloxy, pyrrolidin-1-yl-carbonyl-C_1-3-alkyloxy, piperidin-1-yl-carbonyl-C_1-3-alkyloxy, morpholin-4-yl-carbonyl-C_1-3-alkyloxy, piperazin-1-yl-carbonyl-C_1-3-alkyloxy or 4-(C_1-3-alkyl)-piperazin-1-yl-carbonyl-C_1-3-alkyloxy group,

a hydroxy-C_1-3-alkyl, C_1-3-alkyloxy-C_1-3-alkyl, amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl, di-(C_1-3-alkyl)-amino-C_1-3-alkyl, pyrrolidin-1-yl-C_1-3-alkyl, piperidin-1-yl-C_1-3-alkyl, morpholin-4-yl-C_1-3-alkyl, piperazin-1-yl-C_1-3-alkyl or 4-(C_1-3-alkyl)-piperazin-1-yl-C_1-3-alkyl group,

a hydroxy-C_1-3-alkyloxy, C_1-3-alkyloxy-C_1-3-alkyloxy, C_1-3-alkylsulphanyl-C_1-3-alkyloxy, C_1-3-alkylsulphinyl-C_1-3-alkyloxy, C_1-3-alkylsulphonyl-C_1-3-alkyloxy, amino-C_1-3-alkyloxy, C_1-3-alkylamino-C_1-3-alkyloxy, di-(C_1-3-alkyl)-amino-C_1-3-alkyloxy, pyrrolidin-1-yl-C_1-3-alkyloxy, piperidin-1-yl-C_1-3-alkyloxy, morpholin-4-yl-C_1-3-alkyloxy, piperazin-1-yl-C_1-3-alkyloxy or 4-(C_1-3-alkyl)-piperazin-1-yl-C_1-3-alkyloxy group,

a mercapto, C_1-3-alkylsulphanyl, C_1-3-alkysulphinyl, C_1-3-alkylsulphonyl, C_1-3-alkylsulphonyloxy, arylsulphonyloxy, trifluoromethylsuiphanyl, trifluoromethyl-suiphinyl or trifluoromethylsulphonyl group,

a sulpho, aminosulphonyl, C_1-3-alkyl-aminosulphonyl, di-(C_1-3-alkyl)-aminosulphonyl, pyrrolidin-1-yl-sulphonyl, piperidin-1-yl-sulphonyl, morpholin-4-yl-sulphonyl, piperazin-1-yl-sulphonyl or 4-(C_1-3-alkyl)-piperazin-1-yl-sulphonyl group,

a methyl or methoxy group substituted by 1 to 3 fluorine atoms,

an ethyl or ethoxy group substituted by 1 to 5 fluorine atoms,

a C_2-4-alkenyl or C_2-4-alkynyl group,

a C_3-4-alkenyloxy or C_3-4-alkynyloxy group,

a C_3-6-cycloalkyl or C_3-6-cycloalkyloxy group,

a C_3-6-cycloalkyl-C_1-3-alkyl or C_3-6-cycloalkyl-C_1-3-alkyloxy group or

an aryl, aryloxy, aryl-C_1-3-alkyl or aryl-C_1-3-alkyloxy group,

R¹¹ and R¹², which may be identical or different, in each case represent a hydrogen atom, a fluorine, chlorine, bromine or iodine atom, a C_1-3-alkyl, trifluoromethyl, hydroxy, C_1-3-alkyloxy or cyano group, or

R¹¹ together with R¹², if these are bound to adjacent carbon atoms, also denotes a methylenedioxy, difluoromethylenedioxy, ethylenedioxy or a straight-chain C_3-5-alkylene group and

R¹³ denotes a hydrogen atom, a fluorine, chlorine or bromine atom, a trifluoromethyl, C_1-3-alkyl or C_1-3-alkyloxy group,

R² denotes a hydrogen, fluorine or chlorine atom,

a C_1-6-alkyl group,

a C_2-4-alkenyl group,

a C_3-4-alkynyl group,

a C_3-6-cycloalkyl group,

a C_3-6-cycloalkyl-C_1-3-alkyl group,

a tetrahydrofuran-3-yl, tetrahydropyran-3-yl, tetrahydropyran-4-yl, tetrahydrofuranylmethyl or tetrahydropyranylmethyl group,

an aryl group,

an aryl-C_1-4-alkyl group,

an aryl-C_2-3-alkenyl group,

an arylcarbonyl group,

an arylcarbonyl-C_1-2-alkyl group,

a heteroaryl group,

a heteroaryl-C_1-3-alkyl group,

a furanylcarbonyl, thienylcarbonyl, thiazolylcarbonyl or pyridylcarbonyl group,

a furanylcarbonylmethyl, thienylcarbonylmethyl, thiazolylcarbonylmethyl or pyridylcarbonylmethyl group,

a C_1-4-alkyl-carbonyl group,

a C_1-4-alkyl-carbonyl-C_1-2-alkyl group,

a C_3-6-cycloalkyl-carbonyl group,

a C_3-6-cycloalkyl-carbonyl-C_1-2-alkyl group,

an aryl-A or aryl-A-C_1-3-alkyl group, where A denotes an oxygen or sulphur atom, an imino, C_1-3-alkylimino, sulphinyl or sulphonyl group,

a group R_b, where

R_b denotes a cyano, carboxy, C_1-3-alkyloxy-carbonyl, aminocarbonyl, C_1-3-alkylamino-carbonyl, di-(C_1-3-alkyl)-amino-carbonyl, pyrrolidin-1-ylcarbonyl, piperidin-1-ylcarbonyl, morpholin-4-ylcarbonyl, piperazin-1-ylcarbonyl, 4-methylpiperazin-1-ylcarbonyl, 4-ethylpiperazin-1-ylcarbonyl, hydroxy, mercapto, C_1-3-alkyloxy, C_1-3-alkylsulphenyl, C_1-3-alkylsulphinyl, C_1-3-alkylsulphonyl, amino, C_1-3-alkylamino, di-(C_1-3-alkyl)-amino, pyrrolidin-1-yl, piperidin-1-yl, morpholin-4, yl, piperazin-1-yl, 4-methyl-piperazin-1-yl or 4-ethyl-piperazin-1-yl group,

or a C_1-4-alkyl group substituted by a group R_b, where R_b is as hereinbefore defined,

Y denotes a nitrogen atom,

R³ denotes a C_3-4-alkyl group,

a C_1-3-alkyl group substituted by a group R_c where

R_c denotes a C_3-7-cycloalkyl group optionally substituted by one or two C_1-3-alkyl groups,

a C_5-7-cycloalkenyl group optionally substituted by one or two C_1-3-alkyl groups,

an aryl group or

a furanyl, thienyl, oxazolyl, isoxazolyl, thiazolyl, isothiazolyl, pyridyl, pyridazinyl, pyrimidyl or pyrazinyl group, while the above mentioned heterocyclic groups may each be substituted by one or two C_1-3-alkyl groups or by a fluorine, chlorine, bromine or iodine atom or by a trifluoromethyl, cyano or C_1-3-alkyloxy group,

a C_3-8-alkenyl group,

a C_3-6-alkenyl group substituted by a fluorine, chlorine or bromine atom or by a trifluoromethyl group,

a C_3-8-alkynyl group,

an aryl group or

an aryl-C_2-4-alkenyl group,

and

R⁴ denotes an azetidin-1-yl or pyrrolidin-1-yl group which is substituted in the 3 position by an amino, C_1-3-alkylamino or a di-(C_1-3-alkyl)amino group and may additionally be substituted by one or two C_1-3-alkyl groups,

a piperidin-1-yl or hexahydroazepin-1-yl group which is substituted in the 3 position or in the 4 position by an amino, C_1-3-alkylamino or a di-(C_1-3-alkyl)amino group and may additionally be substituted by one or two C_1-3-alkyl groups,

a 3-amino-piperidin-1-yl group wherein the piperidin-1-yl-moiety is additionally substituted by an aminocarbonyl, C_1-2-alkyl-aminocarbonyl, di-(C_1-2-alkyl)aminocarbonyl, pyrrolidin-1-yl-carbonyl, (2-cyano-pyrrolidin-1-yl-)carbonyl, thiazolidin-3-yl-carbonyl, (4-cyano-thiazolidin-3-yl)carbonyl, piperidin-1-ylcarbonyl or morpholin-4-ylcarbonyl group,

a 3-amino-piperidin-1-yl group wherein the piperidin-1-yl moiety in the 4 position or in the 5 position is additionally substituted by a hydroxy or methoxy group,

a 3-amino-piperidin-1-yl group wherein the methylene group in the 2 position or in the 6 position is replaced by a carbonyl group,

a piperidin-1-yl or hexahydroazepin-1-yl group substituted in the 3 position by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino-group, wherein in each case two hydrogen atoms on the carbon skeleton of the piperidin-1-yl or hexahydroazepin-1-yl-group are replaced by a straight-chain alkylene bridge, this bridge containing 2 to 5 carbon atoms if the two hydrogen atoms are located on the same carbon atom, or 1 to 4 carbon atoms, if the hydrogen atoms are located on adjacent carbon atoms, or 1 to 4 carbon atoms, if the hydrogen atoms are located on carbon atoms which are separated by one atom, or 1 to 3 carbon atoms if the two hydrogen atoms are located on carbon atoms separated by two atoms,

an azetidin-1-yl, pyrrolidin-1-yl, piperidin-1-yl or hexahydroazepin-1-yl group which is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)-amino-C_1-3-alkyl group,

a piperazin-1-yl or [1,4]diazepan-1-yl group optionally substituted at the carbon skeleton by one or two C_1-3-alkyl groups,

a 3-imino-piperazin-1-yl, 3-imino-[1,4]diazepan-1-yl or 5-imino-[1,4]diazepan-1-yl group optionally substituted at the carbon skeleton by one or two C_1-3-alkyl groups,

a [1,4]diazepan-1-yl group optionally substituted by one or two C_1-3-alkyl groups, which is substituted in the 6 position by an amino group,

a C_3-7 cycloalkyl group which is substituted by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group,

a C_3-7-cycloalkyl group which is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)amino-C_1-3-alkyl group,

a C_3-7-cycloalkyl-C_1-2-alkyl group wherein the cycloalkyl moiety is substituted by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group,

a C_3-7-cycloalkyl-C_1-2-alkyl group wherein the cycloalkyl moiety is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)amino-C_1-3-alkyl group,

a C_3-7-cycloalkylamino group wherein the cycloalkyl moiety is substituted by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group, while the two nitrogen atoms at the cycloalkyl moiety are separated from one another by at least two carbon atoms,

an N—(C_3-7-cycloalkyl)-N—(C_1-3-alkyl)-amino group wherein the cycloalkyl moiety is substituted by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group, while the two nitrogen atoms at the cycloalkyl moiety are separated from one another by at least two carbon atoms,

a C_3-7-cycloalkylamino group wherein the cycloalkyl moiety is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)amino-C_1-3-alkyl group,

an N—(C_3-7-cycloalkyl)-N—(C_1-3-alkyl)-amino group wherein the cycloalkyl moiety is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)amino-C_1-3-alkyl group,

a C_3-7-cycloalkyl-C_1-2-alkyl-amino group wherein the cycloalkyl moiety is substituted by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group,

an N—(C_3-7-cycloalkyl-C_1-2-alkyl)-N—(C_1-2-alkyl)-amino group wherein the cycloalkyl moiety is substituted by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group,

a C_3-7-cycloalkyl-C_1-2-alkyl-amino group wherein the cycloalkyl moiety is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)amino-C_1-3-alkyl group,

an N—(C_3-7-cycloalkyl-C_1-2-alkyl)-N—(C_1-2-alkyl)-amino group wherein the cycloalkyl moiety is substituted by an amino-C_1-3-alkyl, C_1-3-alkylamino-C_1-3-alkyl or a di-(C_1-3-alkyl)amino-C_1-3-alkyl group,

a R¹⁹-C_2-4-alkylamino group wherein R¹⁹ is separated from the nitrogen atom of the C_2-4-alkylamino moiety by at least two carbon atoms and

R¹⁹ denotes an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)-amino group,

an R¹⁹-C_2-4-alkylamino group wherein the nitrogen atom of the C_2-4-alkylamino moiety is substituted by a C_1-3-alkyl group and R¹⁹ is separated from the nitrogen atom of the C_2-4-alkylamino moiety by at least two carbon atoms, while R¹⁹ is as hereinbefore defined,

an amino group substituted by the group R²⁰ wherein

R²⁰ denotes an azetidin-3-yl, azetidin-2-ylmethyl, azetidin-3-ylmethyl, pyrrolidin-3-yl, pyrrolidin-2-ylmethyl, pyrrolidin-3-ylmethyl, piperidin-3-yl, piperidin-4-yl, piperidin-2-ylmethyl, piperidin-3-ylmethyl or piperidin-4-ylmethyl group, while the groups mentioned for R²⁰ may each be substituted by one or two C_1-3-alkyl groups,

an amino group substituted by the group R²⁰ and a C_1-3-alkyl group wherein R²⁰ is as hereinbefore defined, while the groups mentioned for R²⁰ may each be substituted by one or two C_1-3-alkyl groups,

an R¹⁹—C_3-4-alkyl group wherein the C_3-4-alkyl moiety is straight-chained and may additionally be substituted by one or two C_1-3-alkyl groups, while R¹⁹ is as hereinbefore defined,

a 3-amino-2-oxo-piperidin-5-yl or 3-amino-2-oxo-1-methyl-piperidin-5-yl group,

a pyrrolidin-3-yl, piperidin-3-yl, piperidin-4-yl, hexahydroazepin-3-yl or hexahydroazepin-4-yl group which is substituted in the 1 position by an amino, C_1-3-alkylamino or di-(C_1-3-alkyl)amino group,

or an azetidin-2-yl-C_1-2-alkyl, azetidin-3-yl-C_1-2-alkyl, pyrrolidin-2-yl-C_1-2-alkyl, pyrrolidin-3-yl, pyrrolidin-3-yl-C_1-2-alkyl, piperidin-2-yl-C_1-2-alkyl, piperidin-3-yl, piperidin-3-yl-C_1-2-alkyl, piperidin-4-yl or piperidin-4-yl-C_1-2-alkyl group, while the above mentioned groups may each be substituted by one or two C_1-3-alkyl groups,

while by the aryl groups mentioned in the definition of the above groups are meant phenyl or naphthyl groups which may be mono- or disubstituted by R_h, while the substituents may be identical or different and R_h denotes a fluorine, chlorine, bromine or iodine atom, a trifluoromethyl, cyano, nitro, amino, aminocarbonyl, aminosulphonyl, methylsulphonyl, acetylamino, methylsulphonylamino, C_1-3-alkyl, cyclopropyl, ethenyl, ethynyl, hydroxy, C_1-4-alkyloxy, difluoromethoxy or trifluoromethoxy group,

by the heteroaryl groups mentioned in the definition of the above groups are meant a pyrrolyl, furanyl, thienyl, pyridyl, indolyl, benzofuranyl, benzothiophenyl, quinolinyl or isoquinolinyl group,

or a pyrrolyl, furanyl, thienyl or pyridyl group, wherein one or two methyne groups are replaced by nitrogen atoms,

or an indolyl, benzofuranyl, benzothiophenyl, quinolinyl or isoquinolinyl group, wherein one to three methyne groups are replaced by nitrogen atoms,

and the above mentioned heteroaryl groups may be mono- or disubstituted by R_h, while the substituents may be identical or different and R_h is as hereinbefore defined,

while, unless otherwise stated, the above mentioned alkyl, alkenyl and alkynyl groups may be straight-chain or branched,

and the hydrogen atoms of the methyl or ethyl groups contained in the definitions may be wholly or partly replaced by fluorine atoms,

the tautomers, enantiomers, diastereomers, the mixtures thereof, the prodrugs thereof and the salts thereof;

wherein the prodrugs thereof are the above compounds:

wherein a carboxy group in the compound is replaced by a group which can be converted in vivo into a carboxy group, selected from: a hydroxymethyl group; a carboxy group esterified with an alcohol wherein the alcohol moiety is a C_1-6-alkanol, a phenyl-C_1-3-alkanol, or a C_3-9-cycloalkanol, where a C_5-8-cycloalkanol may additionally be substituted by one or two C_1-3-alkyl groups, a C_5-8-cycloalkanol wherein a methylene group in the 3 or 4 position is replaced by an oxygen atom or by an imino group optionally substituted by a C_1-3-alkyl, phenyl-C_1-3-alkyl, phenyl-C_1-3-alkyloxycarbonyl or C_2-6-alkanoyl group and the cycloalkanol moiety may additionally be substituted by one or two C_1-3-alkyl groups, a C_4-7-cycloalkenol, a C_3-5-alkenol, a phenyl-C_3-5-alkenol, a C_3-5-alkynol or phenyl-C_3-5-alkynol with the proviso that no bonds to the oxygen atom start from a carbon atom which carries a double or triple bond, a C_3-8-cycloalkyl-C_1-3-alkanol, a bicycloalkanol with a total of 8 to 10 carbon atoms which may additionally be substituted in the bicycloalkyl moiety by one or two C_1-3-alkyl groups, a 1,3-dihydro-3-oxo-1-isobenzofuranol or an alcohol of formula

R_p—CO—O—(R_qCR_r)—OH,

 wherein

R_p denotes a C_1-8-alkyl, C_5-7-cycloalkyl, C_1-8-alkyloxy, C_5-7-cycloalkyloxy, phenyl or phenyl-C_1-3-alkyl group,

R_q denotes a hydrogen atom, a C_1-3-alkyl, C_5-7-cycloalkyl or phenyl group and

R_r denotes a hydrogen atom or a C_1-3-alkyl group;

or

wherein a carboxy group in the compound is replaced by a group which is negatively charged under physiological conditions selected from: a tetrazol-5-yl, phenylcarbonylaminocarbonyl, trifluoromethylcarbonylaminocarbonyl, C_1-6-alkylsulphonylamino, phenylsulphonylamino, benzylsulphonylamino, trifluoromethyl-sulphonylamino, C_1-6-alkylsulphonylaminocarbonyl, phenylsulphonylaminocarbonyl, benzylsulphonylaminocarbonyl or perfluoro-C_1-6-alkylsulphonylaminocarbonyl group;

or

wherein an imino or amino group in the compound is replaced by an amino or imino group substituted with a group which can be cleaved from the imino or amino group in vivo, selected from: a hydroxy group; an acyl group; a phenylcarbonyl group optionally mono- or disubstituted by fluorine, chlorine, bromine or iodine atoms, or by C_1-3-alkyl or C_1-3-alkyloxy groups, while the substituents may be identical or different; a pyridinoyl group; a C_1-16-alkanoyl group; a 3,3,3-trichloropropionyl group; an allyloxycarbonyl group; a C_1-16-alkyloxycarbonyl or C_1-16-alkylcarbonyloxy group, wherein hydrogen atoms may be wholly or partially replaced by fluorine or chlorine atoms; a phenyl-C_1-6-alkyloxycarbonyl group; a 3-amino-propionyl group wherein the amino group may be mono- or disubstituted by C_1-6-alkyl or C_3-7-cycloalkyl groups and the substituents may be identical or different; a C_1-3-alkylsulphonyl-C_2-4-alkyloxycarbonyl, C_1-3-alkyloxy-C_2-4-alkyloxy-C_2-4-alkyloxycarbonyl, R_p—CO—O—(R_qCR_r)—O—CO, C_1-6-alkyl-CO—NH—(R_sCR_t)—O—CO or C_1-6-alkyl-CO—O—(R_sCR_t)—(R_sCR_t)—O—CO group, wherein R_p, R_q and R_r are as hereinbefore defined, and wherein R_s, and R_t, which may be identical or different, denote hydrogen atoms or C_1-3-alkyl groups.