Disclosed is a multiplex ethylene coplymer comprising (a) 50 to 94.8 mole % of units derived from ethylene, which are represented by the following formula (I):--CH.sub.2 --CH.sub.2 -- (I)(b) 5 to 45 mole % of units derived from a monomer selected from alkyl acrylates, alkyl methacrylates, vinyl carboxylates and isopropenyl carboxylates, which are represented by the following formula (II): ##STR1## wherein R.sub.1 stands for a hydrogen atom or a methyl group, and X is ##STR2## in which R.sub.2 and R.sub.3 stand for an alkyl group having 1 to 10 carbon atoms), and (c) 0.2 to 5 mole % of units derived from a monomer having a radical-polymerizable ethylenic double bond and at least one carbon-to-carbon double bond which is different from a double bond of an aromatic nucleus. This ethylene copolymer can be easily cured, and the cured copolymer is a rubber having excellent oil resistance and heat resistance.This multiplex ethylene copolymer can be obtained by copolymerizing a monomer forming the units (a) with a monomer forming the units (b) and (c') a monomer having a radical-polymerizable ethylenic double bond and an acid anhydride group, a carboxyl group and/or an epoxy group, and modifying the obtained copolymer with a low-molecular-weight modifier selected from unsaturated amines and unsaturated alcohols having at least one carbon-to-carbon double bond different from a double bond of an aromatic nucleus (when a radical-polymerizable monomer having an epoxy group is used, the low-molecular-weight modifier may be an unsaturated carboxylic acid having at least one carbon-to-carbon double bond different from a double bond of an aromatic nucleus).