Transition and relaxation processes of polyethylene (PE), polypropylene (PP), and polystyrene (PS) were studied by the positron annihilation technique. From measurements of lifetime spectra of positrons as a function of temperature, the lifetime of ortho-positronium, tau(3), and its intensity, I-3, were found to increase above 260 K for PP. This fact was attributed to a cooperative motion of large segments of molecules above the glass transition temperature, T-g. For PE, above T-g (140 K), the value of tau(3) increased, but the temperature coefficient of I-3 was negative below 230 K. From this fact, for PE, the molecular motions that cause the glass transition were associated with a rearrangement of molecules by local motions such as kink motions. The discrepancy between the results for PE and PP was attributed to the presence of methyl groups in PP and the resultant suppression of the local motions. For PS (T-g = 340 K), the molecular motions were found to start above 260 K, but those were suppressed by an interphenyl correlation. Detailed annihilation characteristics of positrons in polymers were also discussed.