2-Oxo-1-pyrrolidinylalkylcarboxylic acid amides of formula I ##STR1## in which R represents a hydrogen atom or hydroxy group, R.sub.1 represents a hydrogen atom or a methyl group and R.sub.2 represents a substituted or unsubstituted pyridyl group or a substituted phenyl group, the substitution being by from 1 to 3 substituents, which may be the same or different selected from halogen atoms, trifluoromethyl, nitro and acetyl groups, straight or branched-chain alkyl groups having 1-4 carbon atoms, alkoxy groups having 1-4 carbon atoms, straight or branched-chain alkylmercapto groups having 1-7 carbon atoms, substituted alkylmercapto groups of the general formula II ##STR2## in which n represents 1 or 2, R.sub.3 is a hydrogen atom or a methyl group and R.sub.4 is a hydroxy group or an amino group of the general formula V ##STR3## in which R.sub.8 represents a hydrogen atom or methyl group and R.sub.9 represents a methyl group or substituted or unsubstituted benzyl group, or R.sub.8 and R.sub.9 together with the nitrogen atom shown in formula V, form a substituted pyrrolidine ring; sulphonyl groups of the general formula III--SO.sub.2 R.sub.5 IIIin which R.sub.5 represents an --NH.sub.2 group or an alkyl group having 1-3 carbon atoms; and aminoethoxycarbonyl groups of the general formula IV ##STR4## in which each of R.sub.6 and R.sub.7, which may be the same or different, represents a hydrogen atom or methyl or ethyl group; and the pharmaceutically tolerable acid addition salts of compounds of formula I having a basic nitrogen atom are useful in treating cerebral circulatory disturbances, cerebro-atrophic crises and cerebral ageing processes.