Recently novel current-driven resonant states characterized by the π-phase kinks were proposed in numerical and analytic studies on THz wave emission from intrinsic Josephson junctions based on the coupled sine-Gordon equation. In these states hysteresis behavior is observed with respect to the application process of current, and such behavior is due to nonlinearity in the Josephson coupling term. Varying the strength of the critical current, there exists a critical strength for the hysteresis behavior in the fundamental mode and at the critical strength the applied current at the emission peak coincides with the critical one, which means breakdown of superconductivity in actual systems. In higher-harmonic modes in the vicinity of the critical current, the strength of hysteresis becomes small and emission can be observed in the reverse process. Such "quasi-reversible" behavior may explain "reversible emission" reported in a recent experiment.