The present invention relates to a novel ethylene/pentene-1 copolymer whose molded film has a good balance between impact resistance and tear properties and high transparency, also is prominently reduced in a variation of the transparency even after subjected to a heat treatment, and further shows high blocking resistance, provided that the copolymer fulfills specific requisites. The invention also relates to a process for the preparation of the above-mentioned ethylene/pentene-1 copolymer and a formulation of the ethylene/pentene-1 copolymer composition using a stabilizer. According to the invention, there can be obtained an ethylene/pentene-1 copolymer composition which is excellent in heat stability in the molding stage, long-term heat stability and weatherability.