To provide a fluorocopolymer elastomer which is peroxide-curing and exhibits good compression set properties merely when subjected to primary vulcanization.

This elastomer is produced by subjecting a monomer mixture (100mol%) comprising about 50-80mol% vinylidene fluoride, about 15-50mol% hexafluoropropene, and about 30-0mol% tetrafluoroethylene or comprising about 50-85mol% vinylidene fluoride, about 5-50mol% perfluorovinyl ether represented by the formula: CF2=CFORf (wherein Rf is 1-10C perfluoroalkyl or a perfluorooxyalkylene group having at least one ether bond in the carbon chain), and about 50-0mol% tetrafluoroethylene to copolymn. in the presence of about 0.05-1.0mol % iodotrifluoroethylene as a comonomer so that the molecular terminals have iodine atoms bonded thereto.