Solutions of the reactor kinetics equations for the reactivity variation required to achieve specified power responses are presented. This inverse approach is shown to extend the physical understanding of reactor behavior, to have utility in reactor operations, and to admit closed solutions for many otherwise non-linear problems. The inverse method is demonstrated by several examples: heating of a reactor at constant power, a ramp power rise followed by a constant level or by a linear drop, an oscillatory power, and a smooth transition betwen levels. Effects of a negative temperature coefficient may be described in terms of an additional fictitious delayed group. The constant-period response is shown to be optimum for a transition between two power levels.