The proton spin-spin relaxation times (T-2(H)) at different temperatures (from 160 to 390 K) have been determined for polystyrene (PS) and four-arm star styrene-butadiene block copolymer (SB-4A) and its blends with PS of different molecular weights (M(PS)). The results indicate that for PS these exists a crystallinelike structure in its bulk resulting from the microsegregation of phenyl groups, and the transition behavior of PS chains in the "crystalline" state is quite different from that in the "noncrystalline" state; for SB-4A there is a low critical temperature, below which both PS block and PBD chain motions are frozen in, exhibiting characteristics similar to that of an "ideal solid"; for PB/SB-4A blends there is a high critical temperature, above which diffusion of the PS chains into the PBD microdomains was observed. The lower the M(PS) of PS added, the larger its diffusivity D under the same condition. Meanwhile, both the high and low transition temperatures of PS and PBD blocks in the blends strongly depend on the M(PS) Of PS added, indicating the effect of molecular weight of PS on the miscibility and molecular motions of PS/SB-4A blends.