Five new metal-carboxylate chain-based laminated compounds, namely, (2)(infinity)[Fe-II(e,e-trans-1,2-chdc)] (3) (1,2-chdc = cyclohexane-1,2-dicarboxylate), (2)(infinity)[Ni-II(mu-OH2)(e,a-cis-1,2-chdc)] (4), (2)(infinity)[Co-II(mu-OH2)(1,2-chedc)] (5) (1,2-chedc = cyclohex-1-ene-1,2-dicarboxylate), (2)(infinity)[Co-5(II)(mu(3)-OH)(2)(OH2)(2)(1,2-chedc)(4)] (6), and (2)(infinity)[Co-II(4-Me-1,2-chdc)] (7) (4-Me-1,2-chdc = = trans-4-methylcyclohexane-1,2-dicarboxylate) have been hydrothermally synthesized. In these series of magnetic chain-based compounds, 3 and 7 have the same dimeric paddle-wheel M(II)-carboxylate chain as the previously reported compound, (2)(infinity)[Co-II(trans-1,2-chdc)] (2). However, compound 3 does not behave as a single-chain magnet (SCM) but simply an alternating ferro-antiferro magnetic chain. Compound 4 has the cis conformation of 1,2-chdc ligand, which leads to a uniform aqua-carboxylate-bridged Ni(II) chain. Such a Ni-O chain exhibits strong antiferromagnetic interactions, leading to a diamagnetic ground state. Compound 5 features a corner-sharing triangular chain, or A-chain, which is part of a Kagome lattice. However, 5 does not exhibit a spin-frustrated effect but simply spin competition. Compound 6 has a unique pentanuclear Coll cluster, which is further connected by the syn-anti carboxylate into a chain structure. Compound 6 exhibits antiferromagnetic interactions among the Co(II) ions, and no SCM behavior is observed. These results might indicate that the dimeric paddle-wheel Co(II)-carboxylate chain is essential in obtaining SCM behavior in this family of compounds. Although 2 and 7 have very similar SCM behavior, alternating current magnetic studies show that 7 has a higher energy barrier than that of 2. Such behavior is probably caused by the larger anisotropic energy barrier in 7.