Abstract: 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.