The reaction of various CuII salts with 2,5-bis(3-pyridyl)-1,3,4-oxadiazole (L) in CH3CN-H2O medium affords different complexes, the solid structures of which are controlled only by the choice of the counteranions. Reaction of Cu-(ClO4)2.6H2O or Cu(NO3)2.3H2O and L yields the novel bimetallic macrocyclic complex [Cu2L2(H2O)6](ClO4)4(H2O)4 (1) [monoclinic, space group P21/m, a = 8.745(5) A, b = 16.179(10) A, c = 14.930(8) A, beta = 93.253(10) degrees, Z = 2] or [CuL(NO3)2]2(CH3CN)2 (2) [triclinic, space group P1, a = 7.863(3) A, b = 8.679(3) A, c = 13.375(5) A, alpha = 74.121(5) degrees, beta = 78.407(6) degrees, gamma = 86.307(6) degrees, Z = 1]. However, with the replacement of CuII perchlorate or nitrate salts with CuSO4.5H2O or Cu(OAc)2.H2O in the above reaction, two different one-dimensional (1-D) coordination polymers [[Cu2L2(H2O)6(SO4)2](H2O)6]n (3) [triclinic, space group P1, a = 7.078(3) A, b = 11.565(4) A, c = 12.561(5) A, alpha = 109.511(6) degrees, beta = 105.265(6) degrees, gamma = 94.042(6) degrees, Z = 1] or [[Cu2L(mu-OAc)4]]n (4) [monoclinic, space group C2/c, a = 20.007(7) A, b = 7.506(2) A, c = 16.062(5) A, beta = 108.912(5) degrees, Z = 4] were obtained. These results unequivocally indicate that the nature of the counteranions, which play different roles in each complex, is the key factor governing the structural topologies of them. The magnetic properties of these CuII complexes have been investigated by variable-temperature magnetic susceptibility and magnetization measurements, and the magneto-structural correlation has been analyzed in detail.