A polymer composition obtainable by subjecting a particular crosslinkable polymer composition to dynamic crosslinking. The crosslinkable polymer composition contains. (a) a block copolymer comprising two or more polymer blocks of a vinyl aromatic compound and one or more (hydrogenated) polymer blocks of a conjugated diene; (b) an olefin copolymer having a density of 0.88 to 0.92 g/cm.sup.2 and obtained through copolymerization of ethylene and an .alpha.-olefin having 4 to 12 carbon atoms; (c) a softening agent; and (d) an organic peroxide in respective amounts that satisfy the following relational expressions {circle around (1)} to {circle around (3)}: 0.66.ltoreq.Wb/Wa.ltoreq.4{circle around (1)} 0.ltoreq.Wc/(Wa+Wb+Wc).ltoreq.0.25{circle around (2)} 0.001.ltoreq.Wd/(Wa+Wb+Wc).ltoreq.0.01{circle around (3)} wherein Wa, Wb, Wc and Wd represent the respective amounts (by mass) of the components (a), (b), (c) and (d), that are present in the polymer composition prior to the dynamic crosslinking.The polymer composition of the present invention is based on a thermoplastic elastomer that has various improved properties, including moldability, abrasion resistance, scratch resistance, hydrolysis resistance, softness, rubber elasticity, grip, shock absorbance, oil resistance, lightweightness and mechanical strength, and has these properties in a well-balanced manner.