A process for the preparation of peralkylated amines of the general formula I STR1 in which R1, R2 denote C1 -C200 alkyl, C3 -C8 cycloalkyl, C4 -C20 alkylcycloalkyl, C4 -C20 cycloalkylalkyl, C2 -C20 alkoxyalkyl, aryl, C7 -C20 alkylaryl, C7 -C20 aralkyl, C2 -C8 hydroxyalkyl, C2 -C8 mercaptoalkyl, C8 -C20 phenoxyalkyl, C2 -C8 aminoalkyl, C2 -C8 (NHR4)alkyl, C2 -C8 (NR4 R5)alkyl or together form a saturated or unsaturated C2 -C6 alkylene chain optionally mono- to tri-substituted by C1 -C4 alkyl and optionally interrupted by oxygen or nitrogen X denotes a C2 -C20 alkylene or C2 -C20 alkenylene or C4 -C8 cycloalkylene chain optionally mono- to penta-substituted by R3, C1 -C8 alkyl, C1 -C8 alkoxy, C1 -C8 dialkylamino, phenoxy, diphenylamino and/or C2 -C8 alkoxycarbonyl, A denotes hydrogen, C1 -C20 alkyl, C3 -C8 cycloalkyl, C4 -C20 alkylcycloalkyl, C4 -C20 cycloalkylalkyl, C2 -C20 alkoxyalkyl, aryl, C7 -C20 alkylaryl, C7 -C20 aralkyl, C1 -C20 alkoxy, hydroxy, C1 -C20 hydroxyalkyl, amino, C1 -C20 alkylamino, C2 -C20 dialkylamino, C3 -C12 alkenyleneamino, C3 -C8 cycloalkylamino, arylamino, aryl-C1 -C12 alkylamino, halogen, mercapto, C2 -C20 alkenylenoxy, C3 -C8 cycloalkoxy and aryloxy R3 denotes CH2 --NR1 R2, R4, R5 denote C1 -C20 alkyl by the reaction of a nitrile of the general formula II in which R1, R2, R4, R5, X and A have the aforementioned meanings and R3 stands for --CH2 --NR1 R2 or cyano, with a secondary amine of the general formula III STR2 and hydrogen at temperatures ranging from 50° to 250° C. and pressures ranging from 5 to 350 bar in the presence of a catalyst, wherein the catalyst used is palladium on an oxidic support.