A process for producing a modified polyethylene resin, which comprises the step of melt kneading at least: (A) 100 parts by weight of a polyethylene 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 specific functional groups, and (C) from 0.01 to 20 parts by weight of an organic peroxide having a decomposition temperature of from 50 to 115.degree. C., at which temperature a half-life thereof is 1 minute.