The passively mode-locked laser is modeled as a regenerative oscillator. An organic dye used as a saturable absorber is treated as the only nonlinear element in the feedback loop. Using a transcendental equation to represent the transfer function of the inhomogeneously broadened, "energy saturated" dye, numerical analysis shows that a Gaussian pulse is a steady state solution. For the example considered, in which an NdsYAG laser is mode-locked by an Eastman 974 dye, the initial shortening of the pulse by the dye is .6%, and approximately 1 to 2 passes are required to reach steady state.