There is provided a process for producing a modified ethylene-vinylcyclohexane copolymer resin, which comprises the steps of: (1) blending at least the following components (A) to (C) to produce a blend; (A) 100 parts by weight of an ethylene-vinylcyclohexane copolymer resin, (B) from 0.1 to 20 parts by weight of at least one compound selected from the group consisting of: (B1) a compound having in its molecule (i) at least one carbon-carbon double or triple bond and (ii) at least one polar group, and (B2) a compound having in its molecule (iii) an OR group and (iv) at least two same or different functional groups selected from the group consisting of a carboxylic acid group, an acid halide group, an acid anhydride group, an acid halide anhydride group, an acid ester group, an acid amide group, an imide group, an imido group, an amino group and a salt of an amino group, wherein the R is hydrogen, an alkyl group, an aryl group, an acyl group or a carbonyldioxy group, and (C) from 0.01 to 20 parts by weight of an organic peroxide, and (2) melt-kneading said blend in a kneading apparatus to produce a modified thylene-vinylcyclohexane copolymer resin.