N,N-Dibenzylhydroxylamine and other selected hydroxylamine derivatives are effective in stabilizing polyolefin compositions containing a stabilizer or mixture of stabilizers selected from the group consisting of the phenolic antioxidants, the hindered amine light stabilizers, the ultraviolet light absorbers, the organic phosphorus compounds, the alkaline metal salts of fatty acids and the thiosynergists, against degradation upon high temperature extrusion, exposure to the combustion products of natural gas, gamma irradiation or upon storage for extended periods.