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PROBLEM TO BE SOLVED : To obtain a proton-conducting ceramic comprising a new perovskite type crystal structure double oxide containing rare earth elements, alkaline earth elements and scandium, and suitable for a solid electrolytic fuel battery large in a hydrogen concentration battery electromotive force. SOLUTION : This proton-conducting ceramic comprises a perovskite type crystal structure double oxide of formula I or II [R is La, Nd, Sm, Gd; A is Sr, Ca, Ba; M is Mg, Zn; 0=700 deg.C, does not change the ion valence number and has a large hydrogen concentration battery electromotive force.