Abstract: A butenedioic acid monoalkyl ester-copolymerized acrylic elastomer containing 0.1-30% by mole of unreacted butenedioic acid monoalkyl ester on the basis of carboxyl groups copolymerized in the acrylic elastomer or its cross-linkable composition. The cross-linkable composition can give cross-linking products having distinguished vulcanization characteristics and stably showing good compression set characteristics.