The solubility of Nd at the Ba sites and the superconductivity of YBa2−xNdxCu3Oy were investigated by X-ray powder diffraction and measurements of the electrical resistance and ac susceptibility. The single Re123 phase was obtained for x ≤ 0.30. The onset transition temperature T^onc is insensitive to the Nd content x in the region of x ≤ 0.40. All are higher than 95 K. The zero resistance transition temperatures Tzeroc, however, exhibits two-step variation with the increase of x. For x ≤ 0.25, Tzeroc are all above 92 K. The highest T zeroc of 94 K was obtained for x = 0.25. For x ≥ 0.3 Tzeroc drops sharply to about 84 K. Finally T onc falls to 30 K and Tzeroc is below 10 K for x = 0.5. The two-step variation of Tc might be an indication of the existence of two trap levels for holes.