R¹ is a group Ar¹L²Ar²Alk-;

Ar¹ is a naphthyridynyl group optionally substituted with one or more -L³(Alk²)_tL⁴(R⁴)_u atoms or groups;

L³ and L⁴ are each, independently, a covalent bond, —O—, —S—, —C(O)—, —C(O)O—, —OC(O)—, —C(S)—, —S(O)—, —S(O)₂—, —N(R⁸)—, —CON(R⁸)—, —OC(O)N(R⁸)—, —CSN(R⁸)—, —N(R⁸)CO—, —N(R⁸)C(O)O—, —N(R⁸)CS—, —S(O)₂N(R⁸)—, —N(R⁸)S(O)₂—, —N(R⁸)O—, —ON(R⁸)—, —N(R⁸)N(R⁸)—, —N(R⁸)CON(R⁸)—, —N(R⁸)CSN(R⁸)—, or —N(R⁸)SO₂N(R⁸)—;

R⁸ is a hydrogen atom or a straight or branched C_1-6alkyl group optionally substituted with one, two, or three substituents selected from halogen, hydroxy and C_1-6alkoxy;

t is zero or the integer 1;

u is an integer 1, 2 or 3;

Alk² is an aliphatic or heteroaliphatic chain optionally substituted with one or more substituents selected from halogen, —OH, —CO₂H, —CO₂R⁹, —CONHR⁹, —CON(R⁹)₂, —COR⁹, C_1-6alkoxy, thiol, —S(O)R⁹, —S(O)₂R⁹, C_1-6alkylthio, amino, —NHR⁹ and —N(R⁹)₂;

R⁹ is a straight or branched C_1-6alkyl group optionally substituted with one, two, or three substituents selected from halogen, hydroxy and C_1-6alkoxy;

R⁴ is a hydrogen atom; a halogen atom; C_1-6alkyl optionally substituted with one, two, or three substituents selected from halogen, hydroxy and C_1-6alkoxy; C_3-8cycloatkyl optionally substituted with one, two, or three substituents selected from halogen, hydroxy and C_1-6alkoxy; —OR⁵; —SR⁵; —NR⁵R⁶; —NO₂; —CN; —CO₂R⁵; —SO₃H; —SOR⁵; —SO₂R⁵; —SO₃R⁵; —OCO₂R⁵; —CONR⁵R⁶; —OCONR⁵R⁶; —CSNR⁵R⁶; —COR⁵; —OCOR⁵; —N(R⁵)COR⁶; —N(R⁵)CSR⁶; —SO₂N(R⁵)(R⁶); —N(R⁵)SO₂R⁶; N(R⁵)CON(R⁶)(R⁷); —N(R⁵)CSN(R⁶)(R⁷); or —N(R⁵)SO₂N(R⁶)(R⁷), provided that when t is zero and each of L³ and L⁴ is a covalent bond, then u is the integer 1 and R⁴ is other than a hydrogen atom;

R⁵, R⁶, R⁷, and R¹¹ are each, independently, a hydrogen atom or a C_1-6alkyl or C_3-8cycloalkyl group, wherein each of said alkyl and cycloalkyl groups is optionally substituted with one, two, or three substituents selected from halogen, hydroxy and C_1-6alkoxy;

L² is an —N(R⁸)— group;

Ar² is an arylene or heteroarylene group optionally substituted with one or more -L³(Alk²)_tL⁴(R⁴)_u atoms or groups;

Alk is a chain

R is a carboxylic acid (—CO₂H), a carboxylic acid ester (—CO₂Alk⁷), a carbocylic acid amide (—CONR⁵R⁶), a tetrazole, phosphonic acid, phosphinic acid, sulphonic acid, sulphinic acid, boronic acid, or an acylsulphonamide group;

Alk⁷ is a straight or branched C_1-8alkyl group, C_2-8alkenyl group, C_2-8alkynyl group, C_3-8cycloalkyl group, C_3-8heterocycloalkyl group, C_3-8cycloalkylC_1-8alkyl group, C_3-8heterocycloalkylC_1-8alkyl group, C_1-6alkyloxyC_1-6alkyl group, hydroxyC_1-6alkyl group, C_1-6alkylthioC_1-6alkyl group, C_1-6alkylsulfinylC_1-6alkyl group, C_1-6alkylsulfonylC_1-6alkyl group, C_3-8cycloalkyloxyC_1-6alkyl group, C_3-8cycloalkylthioC_1-6alkyl group, C_3-8cycloalkylsulfinylC_1-6alkyl group, C_3-8cycloalkylsulfonylC_1-6alkyl group, C_1-6alkyloxycarbonylC_1-6alkyl group, C_1-6alkyloxycarbonylC_1-6alkenyl group, C_1-6alkyloxycarbonyloxyC_1-6alkyl group, C_1-6alkyloxycarbonyloxyC_1-6alkenyl group, C_3-8cycloalkyloxycarbonyloxyC_1-6alkyl group, N-di-C_1-8alkylaminoC_1-8alkyl group, N—C_6-12aryl-N—C_1-6alkylaminoC_1-6alkyl group, N-di-C_1-8alkyl-carbamoylC_1-8alkyl group, C_6-12arylC_1-6alkyl group, heteroC_6-10arylC_1-6alkyl group, C_6-12aryl group, a C_6-12aryloxyC_1-8alkyl group, a C_6-12arylthioC_1-8alkyl group, a C_6-12arylsulfinylC_1-8alkyl group, a C_6-12arylsulfonylC_1-8alkyl group, C_1-8alkanoyloxyC_1-8alkyl group, C_4-8imidoC_1-8alkyl group, a C_6-12aroyloxyC_1-8alkyl group, or a triglyceride, optionally substituted with one or more R^13a groups;

R^13a is a halogen atom, or an amino (—NH₂), NHR¹⁴, —N(R¹⁴)₂, nitro, cyano, amidino, hydroxyl (—OH), —OR¹⁴, formyl, carboxyl (—CO₂H), esterified carboxyl, thiol (—SH), —SR¹⁴, —SC(═NH)NH₂, —COR¹⁴, —CSR¹⁴, —SO₃H, —SOR¹⁴, —SO₂R¹⁴, —SO₃R¹⁴, —SO₂NH₂, —SO₂NHR¹⁴, SO₂N(R¹⁴)₂, —CONH₂, —CSNH₂, —CONHR¹⁴, —CSNHR¹⁴, —CON(R¹⁴)₂, —CSN(R¹⁴)₂, —N(R¹¹)SO₂R¹⁴, —N(SO₂R¹⁴)₂, —NH(R¹¹)SO₂NH₂, —N(R¹¹)SO₂NHR¹⁴, —N(R¹¹)SO₂N(R¹⁴)₂, —N(R^1l)COR¹⁴, —N(R¹¹)CONH₂, —N(R¹¹)CONHR¹⁴, —N(R¹¹)CON(R¹⁴)₂, —N(R¹¹)CSNH₂, —N(R^1l)CSNHRl14, N(R¹¹)CSN(R¹⁴)₂, —N(R^1l)CSR¹⁴, —N(R¹¹)C(O)OR¹⁴, —SO₂NHet¹, —CONHet¹, —CSNHet¹, —N(R¹¹)SO₂NHet¹, —N(R¹¹)CONHet¹, —N(R¹¹)CSNHet¹, —SO₂N(R¹¹)Het², -Het², —CON(R¹¹)Het², —CSN(R¹¹)Het², —N(R¹¹)CON(R¹¹)Het², —N(R¹¹)CSN(R¹¹)Het², aryl or heteroaryl group;

R¹⁴ is an -Alk⁶(R^13a)m, aryl, or heteroaryl group;

Alk⁶ is a straight or branched C_1-6alkylene, C_2-6alkenylene or C_2-6alkynylene chain, optionally interrupted by one, two or three —O— or —S— atoms or —S(O)p or —N(R¹⁵)— groups;

m is zero or the integer 1, 2 or 3;

p is an integer 1 or 2;

R¹⁵ is a hydrogen atom or C_1-6alkyl group;

Het¹ is a C_5-7cyclicamino group optionally containing one or more —O— or —S— atoms or —N(R¹¹)—, —C(O)—, —C(S)—, S(O) or —S(O)2 groups and optionally substituted with one or more substituents selected from halogen, —OH, —CO₂H, —CO₂R⁹, —CONHR⁹, —CON(R⁹)₂, —COR⁹, C_1-6alkoxy, thiol, —S(O)R⁹, —S(O)₂R⁹, C_1-6alkylthio, amino, —NHR⁹ and —N(R⁹)₂;

Het² is a monocyclic C_5-7carbocyclic group optionally containing one or more —O— or —S— atoms or —N(R¹¹)—, —C(O)— or —C(S)— groups and optionally substituted with one or more substituents selected from halogen, —OH, —CO₂H, —CO₂R⁹, —CONHR⁹, —CON(R⁹)₂, —COR⁹, C_1-6alkoxy, thiol, —S(O)R⁹, —S(O)₂R⁹, C_1-6alkylthio, amino, —NHR⁹ and —N(R⁹)₂;

X is an —O— or —S— atom or an —N(R²)— group;

R² is a hydrogen atom or a C_1-6alkyl group;

V is an oxygen (O) or sulphur (S) atom;

R^z is an atom or group -L¹(Alk¹)_n(R³)_v;

L¹ is a covalent bond, an —O—, —S—, or —Se— atom, or a —C(O)—, —C(O)O—, —OC(O)—, —C(S)—, —S(O)—, —S(O)₂—, —N(R⁸)—, —CON(R⁸)—, —OC(O)N(R⁸)—, —CSN(R⁸)—, —N(R⁸)CO—, —N(R⁸)C(O)O—, —N(R⁸)CS—, —S(O)₂N(R⁸)—, —N(R⁸)S(O)₂-, —N(R⁸)O—, —ON(R⁸)—, —N(R⁸)N(R⁸)—, —N(R⁸)CON(R⁸)—, —N(R⁸)CSN(R⁸)—, or —N(R⁸)SO₂N(R⁸)— group;

Alk¹ is an aliphatic or heteroaliphatic chain optionally substituted with one or more substituents selected from halogen, —OH, —CO₂H, —CO₂R⁹, —CONHR⁹, —CON(R⁹) ₂, —COR⁹, C_1-6alkoxy, thiol, —S(O)R⁹, —S(O)₂R⁹, C_1-6alkylthio amino, —NHR⁹ and —N(R⁹)₂;

R³ is a hydrogen or halogen atom or a group selected from —OR^3a, —SR^3a, —CN and a C_3-10cycloalkyl; C_3-10cycloalkenyl; C_3-10heterocycloalkyl or C_3-10heterocycloalkenyl containing 1, 2, 3 or 4 heteroatoms or heteroatom-containing groups L⁵, where L⁵ is defined as for L³; aromatic or heteroaromatic group optionally substituted with one or more substituents selected from halogen, C_1-6alkyl, haloC_1-6alkyl, —C(OH)(CF₃)₂, C_1-6alkoxy, haloC_1-6alkoxy, thiol, C_1-6alkylthio, —(Alk⁴)gR¹⁰, —CN, —CO₂R¹¹, —NO₂, —CON(R¹¹)₂, —CSN(R¹¹)₂, —COR¹¹, —CSN(R¹¹)₂, —N(R¹¹)COR¹¹, —N(R¹¹)CSR¹¹, —SO₂N(R¹¹)₂, —N(R¹¹)SO₂R¹¹, —N(R¹¹)CON(R¹¹)₂, —N(R¹¹)CSN(R¹¹), N(R¹¹)SO₂N(R¹¹)₂, and phenyl optionally substituted with one, two or three R¹³ groups;

R¹³ is —R^13a or -Alk⁶(R^13a)_m;

Alk⁴ is a straight or branched C_1-3alkylene chain;

g is zero or an integer 1;

R¹⁰ is —OH, —SH, or —N(R¹¹)₂;

R^3a is a hydrogen atom or a straight or branched C_1-6alkyl group or C_3-8cycloalkyl group, wherein each of said alkyl and cycloalkyl groups is optionally substituted with one, two, or three substituents selected from halogen, hydroxy, and C_1-6alkoxy;

n is zero or the integer 1;

v is the integer 1, 2 or 3;

provided that when n is zero and L¹ is a covalent bond, v is the integer 1;

R^X and R^Y, together with the carbon atom to which they are attached, are joined together to form a spiro linked cyclopentyl, cyclohexyl, cycloheptyl, or tetrahydropyranyl group optionally substituted with one or more substituents selected from halogen, C_1-6alkyl, haloC_1-6alkyl, —C(OH)(CF₃)₂, C_1-6alkoxy, haloC_1-6alkoxy, thiol, C_1-6alkylthio, —(Alk⁴)gR¹⁰, —CN, —CO₂R¹¹, —NO₂, —CON(R¹¹)₂, —CSN(R¹¹)₂, —COR¹¹, —CSN(R¹¹)₂, —N(R¹¹)COR¹¹, —N(R¹¹)CSR¹¹, —SO₂N(R¹¹)₂, —N(R¹¹)SO₂R¹¹, —N(R¹¹)CON(R¹¹)₂, —N(R¹¹)CSN(R¹¹), N(R¹¹)SO₂N(R¹¹)₂, and phenyl optionally substituted with one, two or three R¹³ groups;

provided that the compound is other than ethyl (2S)-2-(2-bromo-3-oxo-spiro [3.5 ]non-1-en-1-ylamino)-3-[4-([2,7]naphthyridin-1-ylamino)phenyl]propanoate; or a salt, solvate, hydrate or N-oxide thereof.