Hindered amine light stabilisers (HALS) have been widely studied as effective stabilisers for polyolefins. The mechanism of reaction of HALS with hydroperoxy radicals has been established. We have found that diffusion of HALS to the hydroperoxy site is an important factor in controlling the reaction rate. In an unoxidised polyolefin the polar HALS do not migrate readily. When the polyolefin has a small amount of oxidised groups present the HALS migrate more rapidly. HALS are available with differing numbers of amine groups and of differing size. There is a compromise in effectiveness between these two factors since those with more amines will be more reactive, whereas those with lower molar mass will migrate faster. These processes have been measured using amorphous polyolefins such as poly(styrene-b-ethylene-co-butylene-b-styrene) elastomer (SEBS) and poly(ethylene-co-propylene).