Compounds of the formula I in which R denotes NR 2 R 4, Alk, C(=CH 2)[C(R 4) 2] n Ar 2, Het 2, O[C(R 4) 2] n Ar 2 or OA, X denotes CO or CH 2, Y denotes CO or CH 2, R 1 denotes H, [C(R 4) 2] n Ar 1, (CH 2) n Het, (CH 2) n Cyc, [C(R 4) 2] n COOH, [C(R 4) 2] n CONHAr 1, [C(R 4) 2] n CONH 2, [C(R 4) 2] n NHA, [C(R 4) 2] n NA 2, O[C(R 4) 2] n Ar 1, [C(R 4) 2] n OR 7, [C(R 4) 2] n COO(CH 2) n Ar 1, [C(R 4) 2] n COOA, [C(R 4) 2] n CONH[C(R 4) 2] p CON(R 4) 2 or [C(R 4) n] n CONHCR 4 -[(CH 2) n N(R 4) 2]CON(R 4) 2, R 2 denotes H, [C(R 4) 2] n Ar 2, (CH 2) n COHet 1, (CH 2) n COAr 2, (CH 2) m NA 2 or (CH 2) n Het, R 3 denotes OH or OCOA, R 4 denotes H or alkyl having 1, 2, 3 or 4 C atoms, R 2 and R 4 together also denote alkylene having 2, 3, 4 or 5 C atoms, where a CH 2 group may also be replaced by N(CH 2) m OH or SO 2 R 5, R 6 each, independently of one another, denote H, F or A, R 5 and R 6 together also denote alkylene having 2, 3, 4 or 5 C atoms, where a CH 2 group may also be replaced by NCOA or O, R 7 denotes H or A, Ar 1 denotes phenyl which is unsubstituted or mono-, di-, tri-, tetra- or pentasubstituted by Hal, OH, OA, CONH 2, CONHA, CONA 2, NHSO 2 A, CONHCyc, NHSO 2 Cyc, CONHAr 2, COHet 1 and/or NASO 2 A, Ar 2 denotes phenyl which is unsubstituted or mono-, di-, tri-, tetra- or pentasubstituted by Hal, A, CONH 2 and/or OAr 3, Ar 3 denotes phenyl which is unsubstituted or monosubstituted by NH 2, Het denotes a mono- or bicyclic saturated, unsaturated or aromatic heterocycle having 1 to 4 N and/or O and/or S atoms which is unsubstituted or mono-, di- or trisubstituted by Hal, A, OA, CN, NH 2, NHA, NA 2, NO 2, CN, COOH, COOA, (CH 2) n CONH 2, (CH 2) n CONHA, (CH 2) n CONA 2, NHCOA, COA, CHO, Het 1, SO 2 A, SO 2 NH 2, SO 2 NHA, SO 2 NA 2, CONHNH 2, CONHAr 3, =O and/or Ar 3, Het 1 denotes a monocyclic saturated heterocycle having 1 to 4 N and/or O and/or S atoms which is unsubstituted or mono-, di- or trisubstituted by =O and/or COOA, Het 2 denotes isoindolyl, A denotes unbranched or branched alkyl having 1-10 C atoms, in which 1-7 H atoms may be replaced by F, Cl, Br, OH, CHO, COA, COOA, CN, CONA 2, CONHA and/or CONH 2, and/or in which one or two non-adjacent CH and/or CH 2 groups may be replaced by O, or Cyc, Alk denotes alkenyl having 2, 3, 4, 5 or 6 C atoms, Cyc denotes cyclic alkyl having 3-7 C atoms which is unsubstituted or mono-, di- or trisubstituted by NHCOA, NHSO 2 OH, OA, A, NH 2, NHA, NA 2, COOA, COOH and/or CONHA, Hal denotes F, Cl, Br or I, m denotes 1, 2, 3 or 4, n denotes 0, 1, 2, 3 or 4, p denotes 1, 2 or 3, and pharmaceutically usable salts, tautomers and stereoisomers thereof, including mixtures thereof in all ratios, where the following compounds are excluded: methyl 3-hydroxypiperidine-3-carboxylate, 1-tert-butyl 3-methyl 3-hydroxypiperidine-1,3-dicarboxylate, tert-butyl 3-allyl-3-hydroxypyrrolidine-1-carboxylate, tert-butyl 3-allyl-3-hydroxypiperidine-1-carboxylate. R denotes NR 2 R 4, Alk, C(=CH 2)[C(R 4) 2] n Ar 2, Het 2, O[C(R 4) 2] n Ar 2 or OA, X denotes CO or CH 2, Y denotes CO or CH 2, R 1 denotes H, [C(R 4) 2] n Ar 1, (CH 2) n Het, (CH 2) n Cyc, [C(R 4) 2] n COOH, [C(R 4) 2] n CONHAr 1, [C(R 4) 2] n CONH 2, [C(R 4) 2] n NHA, [C(R 4) 2] n NA 2, O[C(R 4) 2] n Ar 1, [C(R 4) 2] n OR 7, [C(R 4) 2] n COO(CH 2) n Ar 1, [C(R 4) 2] n COOA, [C(R 4) 2] n CONH[C(R 4) 2] p CON(R 4) 2 or [C(R 4) n] n CONHCR 4 -[(CH 2) n N(R 4) 2]CON(R 4) 2, R 2 denotes H, [C(R 4) 2] n Ar 2, (CH 2) n COHet 1, (CH 2) n COAr 2, (CH 2) m NA 2 or (CH 2) n Het, R 3 denotes OH or OCOA, R 4 denotes H or alkyl having 1, 2, 3 or 4 C atoms, R 2 and R 4 together also denote alkylene having 2, 3, 4 or 5 C atoms, where a CH 2 group may also be replaced by N(CH 2) m OH or SO 2 R 5, R 6 each, independently of one another, denote H, F or A, R 5 and R 6 together also denote alkylene having 2, 3, 4 or 5 C atoms, where a CH 2 group may also be replaced by NCOA or O, R 7 denotes H or A, Ar 1 denotes phenyl which is unsubstituted or mono-, di-, tri-, tetra- or pentasubstituted by Hal, OH, OA, CONH 2, CONHA, CONA 2, NHSO 2 A, CONHCyc, NHSO 2 Cyc, CONHAr 2, COHet 1 and/or NASO 2 A, Ar 2 denotes phenyl which is unsubstituted or mono-, di-, tri-, tetra- or pentasubstituted by Hal, A, CONH 2 and/or OAr 3, Ar 3 denotes phenyl which is unsubstituted or monosubstituted by NH 2, Het denotes a mono- or bicyclic saturated, unsaturated or aromatic heterocycle having 1 to 4 N and/or O and/or S atoms which is unsubstituted or mono-, di- or trisubstituted by Hal, A, OA, CN, NH 2, NHA, NA 2, NO 2, CN, COOH, COOA, (CH 2) n CONH 2, (CH 2) n CONHA, (CH 2) n CONA 2, NHCOA, COA, CHO, Het 1, SO 2 A, SO 2 NH 2, SO 2 NHA, SO 2 NA 2, CONHNH 2, CONHAr 3, =O and/or Ar 3, Het 1 denotes a monocyclic saturated heterocycle having 1 to 4 N and/or O and/or S atoms which is unsubstituted or mono-, di- or trisubstituted by =O and/or COOA, Het 2 denotes isoindolyl, A denotes unbranched or branched alkyl having 1-10 C atoms, in which 1-7 H atoms may be replaced by F, Cl, Br, OH, CHO, COA, COOA, CN, CONA 2, CONHA and/or CONH 2, and/or in which one or two non-adjacent CH and/or CH 2 groups may be replaced by O, or Cyc, Alk denotes alkenyl having 2, 3, 4, 5 or 6 C atoms, Cyc denotes cyclic alkyl having 3-7 C atoms which is unsubstituted or mono-, di- or trisubstituted by NHCOA, NHSO 2 OH, OA, A, NH 2, NHA, NA 2, COOA, COOH and/or CONHA, Hal denotes F, Cl, Br or I, m denotes 1, 2, 3 or 4, n denotes 0, 1, 2, 3 or 4, p denotes 1, 2 or 3, methyl 3-hydroxypiperidine-3-carboxylate, 1-tert-butyl 3-methyl 3-hydroxypiperidine-1,3-dicarboxylate, tert-butyl 3-allyl-3-hydroxypyrrolidine-1-carboxylate, tert-butyl 3-allyl-3-hydroxypiperidine-1-carboxylate.