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PROBLEM TO BE SOLVED : To provide a cylindrical solid electrolyte fuel cell capable of preventing separation from a solid electrolyte air electrode, and also manifesting and maintaining a stable output function. SOLUTION : An air electrode 32 is mainly composed of a perovskite complex oxide containing at least La and Mn as metallic elements. In addition, 8 to 10 wt.% of Ca and 10 to 20 wt.% of at least one of rare earth elements are contained on the basis of an oxide conversion value. Also, a low condensation zone 41 containing Ca and at least one of rare earth elements respectively equal to 8 wt.% or less exists on the surface layer of the air electrode 32.