The phases with general formula R1+xNb3O9 (R=La, Ce, Nd, x=0-0.15) were synthesized and studied by X-ray powder diffraction, resistivity and magnetic susceptibility measurements. The homogeneity range of solid solutions increases concomitantly with the increase of the rare-earth cation radius, and it was found to be 0.05 for Nd, 0.1 for Ce and 0.15 for La at 1200-degrees-C. The crystal structure of La1.15Nb3O9 was refined by X-ray powder data. It was found that all La cations occupy only one of two possible cation positions. Resistivity measurements revealed drastic changes of R(T) for increasing x. No diamagnetic effects were detected by susceptibility measurements down to 12K.