Thermally stable olefin polymers are obtained by addition, before or during polymerization, or after polymerization is substantially complete, but before quenching the catalyst, which terminates the polymerization reaction, of stabilizers of the HALS type ("Hindered Amine Light Stabilizer") of monomeric or oligomeric type, containing in the molecule one or more substituted piperidyl groups having formula: ##STR1## wherein R1 are the same or different from each other and are C.sub.1 -C.sub.4 alkyl radicals, tetramethylpiperidyl radicals, or the alkyl radicals, together with the piperidyl carbon atom to which they are bonded, form a C.sub.5 -C.sub.9 cycloalkyl radical; R.sub.2 are the same or different from each other and are hydrogen, C.sub.1 -C.sub.18 alkyl radicals, C.sub.7 -C.sub.18 aralkyl radicals, or said alkyl radicals together with the piperidyl carbon atom to which they are bonded, are a C.sub.5 -C.sub.10 cycloalkyl radical; R.sub.3 are the same or different from each other and are hydrogen, C.sub.1 -C.sub.18 alkyl radicals or C.sub.7 -C.sub.18 aralkyl radicals; R.sub.4 is hydrogen, a C.sub.1 -C.sub.8 alkyl radical or a benzyl radical; Z is hydrogen or an organic radical. Suitable organic radicals include C.sub.1 -C.sub.18 alkyl; C.sub.1 -C.sub.12 alkylene; C.sub.3 -C.sub.12 alkenyl; C.sub.3 -C.sub.5 alkenyl; C.sub.7 -C.sub.18 aralkyl; C.sub.2 -C.sub.4 acyl; C.sub.2 -C.sub.18 alkanoyl; C.sub.3 -C.sub.18 alkoxyalkyl; C.sub.3 -C.sub.18 alkenoyl; oxyl; cyanomethyl, and xylylenyl radicals; a radical having valence from 1 to 4 and containing from 1 to 4 hydroxyl groups and, optionally, containing ether, ester, or heterocyclic groups, all the valences of this radical being bonded to the nitrogen of the piperidyl rings; a bivalent radical containing one or more ester or amide groups, and a radical ##STR2## wherein R.sub.5 and R.sub.6 are hydrocarbyl radicals. Preferably Z is a C.sub.1 -C.sub.12 alkyl, C.sub.3 -C.sub.8 alkenyl, C.sub.7 -C.sub.11 aralkyl, or a bivalent radical containing one or more ester groups wherein the two valences of said radicals are bonded to piperidyl rings.