The influence of the relaxation time of a saturable absorber on the dynamics of a quasi-continuous ring laser is investigated. It is shown that in a dye laser with a fast absorber, bistability arises; thus two multimode regimes coexist. The regime of shallow stochastic modulation is established spontaneously. Transition to the mode-locking regime accompanied by a sharp increase in the number of generated modes is feasible only under the action of an initiating pulse (hard mode locking). The analytical criterion for hard locking has been obtained. If the criterion is not satisfied, the only stable regime of a laser is mode locking. In this case the transient process is the longer the smaller the relaxation time of a saturable absorber.