To provide a fluorinated elastic copolymer composition, and a cross-linked rubber member obtained by crosslinking the fluorinated elastic copolymer composition, which is excellent in hot water resistance and steam resistance under severe conditions.A fluorinated elastic copolymer composition, which comprises a fluorinated elastic copolymer and a compound represented by the following formula (1) wherein the compound represented by the following formula (1) is contained in an amount of from 0.1 to 10 parts by mass per 100 parts by mass of the fluorinated elastic copolymer: (RCOO−)nMn+  (1) (wherein R is a C10-30 organic group, n is an integer of 2 or 3, and M is an alkaline earth metal, Zn, Cd, Co, Sn, Cu, Pb, Ni or Al).