Crystal structure of Ln(2)Ni(1-x)Cu(x)O(4+delta) (Ln= La, Pr, Nd, Sm and Eu), which are expected as new cathode materials for solid fuel cells, was investigated. Single phase with K2NiF4 structure, so-called T-phase, was obtained for La2Ni1-xCuxO4+delta regardless of Cu content. Single phase with Nd2CuO4 structure, so-called T'-phase, was obtained for Sm2Ni1-xCuxO4+delta and Eu2Ni1-xCuxO4+delta for only 0.95 <= x <= 1.0 and x=1.0 respectively. No T-phase was obtained for the other composition of Ln(2)Ni(1-x)Cu(x)O(4+delta) (Ln=Sm, Eu). The single T-phase and T'-phase were obtained for Pr2Ni1-xCuxO4+delta with x <= 0.4 and x=1.0, respectively. For Pr2Ni1-xCuxO4+delta with x between 0.5 and 0.9, phase separation into T-phase and T'-phase due to miscibility gap was observed, showing similar behavior with Nd2Ni1-xCuxO4+delta except for little smaller x range of the miscibility gap. From high temperature X-ray diffraction measurements, it was revealed that the miscibility gap between 0.5 and 0.9 of Pr2Ni1-xCuxO4+delta remained up to 700 degrees C. Variation of the crystal structure of Ln(2)Ni(1-x)Cu(x)O(4+delta) on kinds of Ln and Cu content could be explained by using tolerance factor calculated from ionic radius of Ln(3+), Ni2+ and Cu2+.