A method is proposed for treating depletion effects in a nuclear reactor by a mathematical model in which the time derivative of the neutron flux is retained and the reactor is kept at its desired power level through operation of a control system actuated by any differences between the actual and desired power level. The criticality searches required with the conventional depletion method to find consistent density-temperature profiles, control rod positions, xenon distribution, and flux shapes are thereby avoided. The time-dependent flux, control, and isotopic concentration equations are linearized and solved simultaneously by a numerical procedure that permits time steps as large as those employed with conventional depletion codes. Simple numerical examples that test the essential features of the method are presented.