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We present an analytic and numerical analysis of regenerative oscillation in the lossless nonlinear Fabry-Perot based on a semiclassical model. We show that unstable positive slope regions may exist along all branches of the steady-state transfer curve which lead to regenerative oscillation or to precipitation to lower branches. The stability of these oscillations is analyzed in terms of the dynamic behavior of the nonlinear index. Our analytic expressions for the period, amplitude, waveform, and phase relation of the output intensity and index oscillations are shown to agree with numerical results to better than 10 percent. We investigate the possibility of experimental observation of regenerative oscillation, and show that it may be present under reasonable experimental conditions.