Three compounds of general formula (NBu4)[(MRuIII)-Ru-II(ox)(3)] have been synthesized; NBu4+ stands for tetra-n-butylammonium, M for Mn, Fe, and Cu, and ox(2-) for the oxalate dianion. The X-ray powder patterns for the three derivatives have revealed that these compounds are isostructural with (NBu4)[(MnCrIII)-Cr-II(ox)(3)], whose crystal structure was known, and the cell parameters have been refined in the R3c space group. The (NBu4)[(MRuIII)-Ru-II(ox)(3)] compounds are new examples of two-dimensional bimetallic assemblies with oxalate bridges. The temperature (T) dependences of the magnetic susceptibility (chi(M)) in both the de and ac modes and the field dependences of the magnetization have been investigated. The local spins are S-Ru = S-Cu = 1/2, S-Mn = 5/2, and S-Fe = 2. The Ru-III-M-II interaction has been found to be antiferromagnetic for M = Fe and Cu and ferromagnetic for M = Mn. The two compounds (NBu4)[(FeRuIII)-Ru-II(ox)(3)] and (NBu4)[(CuRuIII)-Ru-II(ox)(3)] exhibit a ferrimagnetic behavior, characterized by a minimum in the chi(M)T versus T plots. (NBu4)[(FeRuIII)-Ru-II(ox)(3)] exhibits a long-range magnetic ordering at T-c = 13 +/- 1 K. A slight frequency dependence of the out-of-phase ac magnetic response has been observed. The field dependence of the magnetization in the magnetically ordered state has revealed a rather strong coercivity, with a coercive field of 1.55 kOe at 2 K. A theoretical model has been used to determine the magnitude of the Ru-III-M-II interactions, with M = Mn and Fe. This model is based on a quantum-classical spin approach together with Monte Carlo simulations. The interaction parameters have been found as J = 1.04 cm(-1) for (NBu4)[(MnRuIII)-Ru-II(ox)(3)] and -9.7 cm(-1) for (NBu4)[(FeRuIII)-Ru-II(ox)(3)], with a spin Hamiltonian of the type -J Sigma(ij)S(Ru,i). S-Mj. The magnetic properties of these compounds have been discussed. In particular, it has been emphasized that the symmetry rules governing the nature and the magnitude of the interaction between two 3d magnetic metal ions seem not to be valid anymore for 4d ions such as Ru-III.