New compounds of the type R(2/3-x)Rh(2)O(4) with the CaFe(2)O(4) structure have been prepared, where R is a rare earth. For crystals grown in a Bi/V/O flux, the rare earth was partially replaced by Bi. No evidence of ordering of the A cation vacancies is found, but the A cations are displaced from the ideal A cation site by about 0.24 A. Electrical conductivity measurements on crystals suggest that the materials are degenerate semiconductors with Seebeck measurements showing p-type behavior. This is consistent with our observation that x in R(2/3-x)Rh(2)O(4) ranges up to about 0.09. The compounds were also characterized by magnetic susceptibility and diffuse reflectance measurements.