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The paper presents a detailed analysis of FM laser oscillation which includes the effect of arbitrary atomic lineshape, saturation, and mode pulling. Such oscillation is achieved by means of an intracavity phase perturbation, and is a parametric oscillation wherein the laser modes oscillate with FM phases and nearly Bessel function amplitudes. One principal idea is that of the competition between different FM oscillations. The effect of the intracavity phase perturbation is to associate a set of sidebands with each of the previously free-running laser modes. While the free-running laser modes experienced their gain from essentially independent atomic populations, the competing FM oscillations to a large extent see the same atomic population; and in cases of interest the strongest of these oscillations is able to quench the competing weaker oscillations and establish the desired steady state condition. Results of the analysis include the following: threshold and power output, amplitudes and phases of all sidebands, frequency pulling of the entire oscillation, time domain behavior, distortion, super-mode conversion efficiency, and effect of mirror motion. Results of numerical application of the theory to a number of specific cases are given.