The synthesis, crystal structure, and magnetic properties of a new series of isostructural rare earth cuprates, RCu(2)O(4) (R = La, Nd, Sm, and Eu), are reported. The highly oxidized materials with an average formal copper oxidation state of Cu-2.5+ were isolated by precipitation from molten NaOH at 400 OC. Powder X-ray diffraction data for EuCu2O4 combined with neutron diffraction data for NdCu2O4 were used to determine the crystal structure and refine the structure by Rietveld profile analysis. The lattice parameters for NdCu2O4 in the non-standard monoclinic space group 12/a derived from the neutron data set are the following : a 5.826(1) Angstrom, b = 9.703(1) Angstrom, c - 5.753(1) Angstrom, and beta = 92.341(1)degrees. The copper-oxygen network consists of a three-dimensional array of CuO4 distorted square planes that are cornered-shared; the Cu-O-Cu bond angle is similar to 115 degrees. These phases exhibit magnetic ordering of the copper spins as determined by a large increase in the magnetization as the temperature is lowered, the onset of which varies between 18 and 28 K, depending on R. While the negative Weiss constants for LaCu2O4 and NdCu2O4 indicate that the predominant interaction is antiferromagnetic, the saturation moments of similar to 0.13 mu(B) per mol of RCu(2)O(4) indicate that there is a significant ferromagnetic component, possibly due to canting of the ordered copper moments.