Preparations, crystal structures, and spectral and magnetic properties of two new chiral one-dimensional cyano-bridged coordination polymers, [Cu(II)L2]M(II)(CN)].2H2O (M(II) = Ni(II) (1) and Pt(II) (2), L = trans-cyclohexane-(1R,2R)-diamine) have been presented. Complex 1 crystallizes in the monoclinic P2(1) space group with a = 9.864(4) A, b = 15.393(8) A, c = 7.995(4) A, beta = 110.32(3) degrees , V = 1138.4(10) A3, and Z = 2, while 2 crystallizes in the monoclinic P2(1) space group with a = 9.899(3) A, b = 15.541(4) A, c = 8.102(2) A, beta = 111.02(2) degrees , V = 1163.6(5) A3, and Z = 2. The unique zigzag cyano-bridged chains along the crystallographic b axis consist of alternate chiral [CuL(2)]2+ cations and square-planar [M(CN)4]2- anions. One side of the axial Cu-N(triple bond C) bond distances are 2.324(6) and 2.34(1) A with Cu-N[triple bond]C angles of 137.8(6) degrees and 138.2(9) degrees for 1 and 2, respectively. On the other hand, the opposite side of the axial Cu-N(triple bond C) bond distances are 3.120(8) and 3.09(1) A with significantly large bent Cu-N[triple bond]C angles of 97.9(5) degrees and 96.8(7) degrees for 1 and 2, respectively. The novel axial bonding features of extremely long semi-coordination Cu-N bonds are attributed to coexistence of pseudo-Jahn-Teller elongation and electrostatic interaction in the unique zigzag cyano-bridged chains. The characteristic bonding features with overlap between small 3d (Ni(II)) or large 5d (Pt(II)) and 3d (Cu(II)) orbitals results in larger shifts in XPS peaks of not only Cu2p(1/2) and Cu2p(3/2) but also Ni2p(1/2) and Ni2p(3/2) for 1 than those of 2, which is also consistent with weak antiferromagnetic interactions with Weiss constants of -5.31 and -5.94 K for 1 and 2, respectively. The d-d, pi-pi*, and CT bands in the electronic, CD, and MCD spectra for 1 and 2 in the solid state at room temperature are discussed from the viewpoint of magneto-optical properties.