The random cycloolefin copolymer compsn. comprises: (A) a random cyclo-olefin copolymer composed of an ethylenic component and a cycloolefin component of formulae (I) and (II), respectively. In the formulae, R1-R10 are, each, H, halogen atom, or hydrocarbon group; n and m are each 0 or positive integers; l is an integer greater than or equal to 3; ; (B) one or more soft copolymers selected from the gp. consisting of (i) random cycloolefin copolymers composed of an ethylenic component, at least one other alpha-olefinic component and a cycloolefin component, (ii) amorphous or weakly crystalline alpha-olefinic elastic copolymers formed by at least two olefins, (iii) elastic alpha-olefin-diene copolymers formed by at least two alpha-olefins and at least one non-conjugated diene, and (iv) aromatic vinyl hydrocarbon-conjugated diene copolymers or their hydrogenation prods., and, if necessary, (C) an organic or inorganic filler. (A) has a limiting viscosity measured at 135 deg.C in decalin of 0.05 to 10 dl/g and a softening temp. (TMA) of 70 deg.C or higher. Component (i) of (B) has a limiting viscosity of 0.01-10 dl/g and a softening temp. lower than 70 deg.C.