The inversion states of a saturated three-level traveling-wave quantum paramagnetic amplifier have been investigated under conditions of bistable resonator pumping. The equations of motion for the vectorial order parameter have been obtained using adiabatic elimination of fast variables. These equations are a generalization of the scalar two-level Drummond model for the case of a three-level quantum active system. Isolated branches of the constant of inversion have been found from stationary solutions of equations for the vectorial order parameter. A analysis of bifurcations in the saturated quantum amplifier with bistable pumping has been represented with full details.The saturation of transitions between quantum levels of active centers is of paramount importance at the excitation of states with inverse population difference of energy levels. This mechanism is the basis for operation of many devices of quantum electronics [1,2] and other equipments of this type (for example, acoustical quantum amplifiers and phasers generators [3,4], radio-frequency masers based on nuclear magnetic resonance [5] and other active systems [6]).The investigation of nonlinear processes in optical quantum systems led to the experimental disclosure of effects of bistability and multistability [7] in the middle 70s. In the case of bistability there are two different stable states of a nonlinear optical resonator at the same set of control parameters. At the multistability there are more than two such stable states. The initial interest in optical bistable systems has been roused by the assumed possibility of their workability as a component basis for computers of a new generation [8], since the switching time between states of a bistable cell of the nonlinear optical resonator can be small (less than 10 -9 s).The microwave analogue of the optical bistability has been also observed in a number of cases in paramagnetic [9] and gas [7,10] operating media in the frequency range from 10 to 85 GHz, however the typical switching times for microwave bistable systems turn out to be much more orders greater than for optical ones. Therefore, to develop computer logic elements, the microwave bistable cells can not be used. Nevertheless the investigation of bistability in microwave systems is not only of scientific interest but sharply defined practical interest although from the absolutely different point of view.The fact is that the ramification of states of a nonlinear system (the bistability and multistability of this phenomenon are particular cases) is the rule rather than the exception, if the corresponding nonlinear parameter C exceeds the specific threshold. For the optical bistable system this threshold is well known = opt C 4, where opt C is the parameter of cooperativity [7,11] being proportional to the resonator figure of merit. The similar threshold exists as well as for the microwave nonlinear resonator that was shown, *