The thermoplastic resin composition (Xi) of the present invention comprises (A1), (B1), (C1), and optionally (D1) below: 1 to 90 wt % of an isotactic polypropylene (A1); 9 to 98 wt % of a propylene/ethylene/.alpha.-olefin copolymer (B1) containing 45 to 89 mol% of propylene-derived structural units, 10 to 25 molt of ethylene-derived structural units, and optionally, 0 to 30 mol% of C.sub.4-C.sub.20 .alpha.-olefin-derived structural units (a1); 1 to 80 wt % of a styrene-based elastomer (C1); and 0 to 70 wt % of an ethylene/.alpha.-olefin copolymer (D1) whose density is in the range of 0.850 to 0.910 g/cm.sup.3, wherein (A1)+(B1)+(C1)+(D1)=100 wt %.