Relaxation processes in polyethylene (PE) and polystyrene (PS) were studied by positron annihilation technique. For PE, above the glass transition temperature, T-g, the size of free volumes and its concentration were increased by the micro-Brownian motion of molecules. For PS, local motions of molecules in backbone chains were found to start above 260 K. However, these local motions were suppressed by an interphenyl correlation. For both PE and PS, below 250-260 K, the formation probability of positronium atoms increased with decreasing temperature. This fact was assigned to the freezing in of the local motions of molecules. For PS, an onset of the local motions of molecules was observed above 100 K. These motions were expected to be associated with liberation of phenyl groups.