The reaction of various Cull 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)2.6H(2)O or Cu(NO3)(2).3H(2)O and L yields the novel bimetallic macrocyclic complex [Cu2L2(H2O)(6)](ClO4)(4)(H2O)(4) (1) [monoclinic, space group P2(1)/m, a = 8.745(5) Angstrom, b = 16.179(10) Angstrom, c = 14.930(8) Angstrom, beta = 93.253(10)degrees, Z = 2] or [CuL(NO3)(2)](2)(CH3CN)(2) (2) [triclinic, space group P (1) over bar, a = 7.863(3) Angstrom, b = 8.679(3) Angstrom, c = 13.375(5) Angstrom, alpha = 74.121 (5)degrees, beta = 78.407(6)degrees, gamma = 86.307(6)degrees, Z = 1]. However, with the replacement of Cu-II perchlorate or nitrate salts with CuSO4.5H(2)O 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 P (1) over bar a = 7.078(3) Angstrom, b = 11.565(4) Angstrom, c = 12.561(5) Angstrom, 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) Angstrom, b = 7.506(2) Angstrom, c = 16.062(5) Angstrom, 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 Cull complexes have been investigated by variable-temperature magnetic susceptibility and magnetization measurements, and the magneto-structural correlation has been analyzed in detail.