Abstract: Phenyl-3-aminoalkyl-4-methyl-2,6-dioxopiperidines of the Formula I ##STR1## wherein: R.sub.1 represents hydrogen or C.sub.1 -C.sub.4 alkyl;n is 1 or 2;R.sub.2 represents hydrogen or methyl, provided that one R.sub.2 is hydrogen when n is 2;R.sub.3 represents hydrogen or C.sub.1 -C.sub.2 alkyl;R.sub.4 representss C.sub.1 -C.sub.2 alkyl;R.sub.5 and R.sub.6 independently represent hydrogen or methyl;m is 0 to 3; andeach Y is in a meta or para position and independently represents hydroxy, C.sub.1 -C.sub.2 alkoxy, C.sub.1 -C.sub.2 alkyl, C.sub.1 -C.sub.2 hydroxyalkyl, halogen, or trifluoromethyl, provided that hydroxy and alkoxy are not in the para position.or pharmacologically acceptable acid addition salt thereof have analgesic activity. The compounds can be administered enterally, parenterally or topically. The topical compositions are novel.The presently preferred compound is 3-(3'methoxyphenyl)-3-(3"-N,N-dimethylaminopropyl)-4,4-dimethyl-2,6-dioxop iperidine (AGN 2979).