In order to investigate the accuracy of approximate solutions for nonlinear vibrations, the complete and approximate solutions were analysed for the forced vibration of a single-degree-of-freedom-system with hysteresis characteristics consisting of a parallelogram. The system was selected so that the complete solution might be obtained. Summarizing the results, the approximate solution is considerably accurate in the vicinity of the resonance point. Under some conditions of hysteresis characteristics, the resonant amplitude becomes infinity in the approximate solution, although it is finite in the complete one. There is some difference between these solutions as to the frequency ratio and the amplitude ratio at the resonance point where finite amplitude exists.