Specific hydrogenated block copolymer composition and process for producing the same

A process for producing a composition comprising,

• (a) 1 to 99 parts by weight of a specific hydrogenated product of a block copolymer having at least one polymer block composed mainly of a vinyl aromatic compound and at least one polymer block composed mainly of a conjugated diene compound, a modified product thereof, which comprises said specific hydrogenated product having grafted thereon 0.01 to 50 parts by weight per 100 parts by weight of the block copolymer of an .alpha.,.beta.-unsaturated carboxylic acid or the anhydride, the esterified product, the amidated product or the imidated product thereof, or a mixture of said product and said modified product, wherein the content of the vinyl aromatic compound prior to hydrogenation is 5 to 95% by weight and the content of vinyl linkages prior to hydrogenation which originated from the conjugated diene compound is 10 to 80%, said product satisfying the following conditions;
• (1) the hydrogenated ratio of the total of aliphatic double bonds which originated from the conjugated diene compound is not lower than 5% and lower than 50%, and
• [B]/[V].sup.1/2 =3 to 20, (2)
• wherein [B] is the hydrogenated ratio of the vinyl linkage portions which originated from the conjugated diene compound, and
• (b) 99 to 1 parts by weight of at least one thermoplastic substance selected from the group consisting of tackifier resins, thermoplastic resins excluding tackifier resins and bituminous materials, which comprises mixing component (a) with component (b).