[Ni1-xCux(tmdt)(2)] (tmdt = trimethylenetetrathiafulvalenedithiolate) was prepared for realizing molecular Kondo systems. Magnetic moments (S = 1/2) are considered to exist at the central {CuS4} parts of Cu(tmdt)(2) molecules. The chi T-versus-T curve of the system with x approximate to 0.15 showed a broad peak at similar to 10 K. The decrease in the chi T value below 10 K is consistent with a singlet ground state, as expected for a Kondo system. However, in the system with x approximate to 0.27, the chi T value decreased when the temperature was lowered to 2 K, indicating antiferromagnetic interactions between magnetic moments through pi-d interactions. Although the susceptibility anomaly suggested that the pi-d interactions become important at T < 20 K, the observed resistivity (rho(obs)) showed no resistivity minimum characteristic of a Kondo system down to 4.2 K. However, the differential resistivity Delta rho(T) = rho(obs) - rho(L)(T) showed a logarithmic resistivity increase at 8-20 K with decreasing temperature, where rho(L)(T) is a fitted function of rho(obs) obtained at T > 50 K that is considered to represent approximately the temperature dependence of the resistivity without spin scattering of the conduction electrons.