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Numerical computer models could be of high value in testing ideas for improving passive mode locking. Most of the known models for solid-state lasers lack realistic quantitative results, however. A new model is presented, using a rate-equation approach which has been refined to include interference effects by using field amplitudes and phases instead of energies. Also, the saturable absorber is treated by rate equations. With this model, a rather complete description of the pulse evolution is possible. The influence of various parameters on the mode-locking quality is calculated. The model is also capable of reliably describing processes based mainly on interference effects, like the action of external subresonators.