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This paper presents a detailed nonlinear analysis of the internally loss-modulated laser including the effect of arbitrary atomic lineshape, saturation, and mode pulling. Results of the analysis are in part numerical and include a study of the spectral and time domain behavior of the laser output. The results include a determination of the minimum perturbation strength which is necessary to produce phase locking, peak pulse amplitude, and minimum pulsewidth as a function of perturbation strength, a consideration of the detuned case, and a comparison of AM- versus FM-type phase locking. Results are compared with the previously obtained linearized solutions of others.