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The theory of an optical pulse generator, consisting of a solid-state laser with a saturable absorber at one end of the cavity, is considered in some detail. Equations are obtained using third-order perturbation theory for the nonlinear medium and Maxwell's equations for the cavity which describe the behavior of the absorber in bringing the modes into phase alignment. Using simplifying assumptions, it is shown that short pulses are a solution of these equations and that they are a stable solution, provided that the dye fluorescence decay time is sufficiently short. We discuss the ability of the device to mode-lock when opposed by dispersion within the cavity. Computer solutions of the full equations for nine coupled modes are obtained, which demonstrate the development of the pulse in real time, and show the effects of cavity dispersion and long dye fluorescence decay time. A suggestion for a shaped-pulse generator is presented. The limitations of this theory, the most stringent of which being the restriction to the regime of validity of perturbation theory, are discussed.