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Metal-organic frameworks showing successive magnetic ordering are far less common than inorganic compounds.Here,we report two metal-organic frameworks[CoⅡ(ox)(bphy)·0.1(DMF)·0.1(MeOH)]n(1)and[CoⅡ3(ox)3(bphy)2(DMF)2],,(2)com-prised of zigzag and necklace CoⅡ-ladders,respectively.Together with a previously reported compound[CoⅡ(ox)(bphy)·0.2(DMF)]n(3)consisting of spiraling zigzag CoⅡ-ladders,these three compounds provide a good system for comparative structural and magnetic studies.Comprehensive magnetic analysis reveals that the three compounds undergo long-range magnetic ordering at～2.6 K but exhibit vastly different short-range magnetic correlations:compound 1 shows short-range spin-canted anti-ferromagnetism ordering at～14.0 K;compound 2 demonstrates successive short-range antiferromagnetism ordering at～15.5 and～12.6 K;compound 3 shows slow magnetic relaxation with Tb≈4.6 K.These results demonstrate long-range magnetic ordering is readily accessible in the frameworks of ox2-bridging CoⅡ-ladders linked by bphy,where short-range magnetic correlations can be systematicly tuned by the CoⅡ-ladder structures.