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By using a simple solid reaction method, we have fabricated alkaline metal doped cobalt oxides Anx CoO2+δ(An = Na, K). The magnetic measurement shows a superconducting-like diamagnetic signal at 31 K based on a strong superparamagnetic signal. Below 31 K, the magnetization hysteresis loops contain a strong rough linear superparamagnetic background and a superconducting hysteresis. The typical magnetization hysteresis loops for a type-Ⅱ superconductor are found. Preliminary resistive data also show a fast dropping of resistance below Tc.These give indication of superconductivity below 31 K in Anx CoO2+δ (An = Na, K).