The generalized perturbation theory was developed to accommodate constant power core depletion. The resulting adjoint equations are distinguished from the corresponding constant flux depletion system by the coupling of adjacent time intervals in the source of the generalized adjoint flux equation. The method is demonstrated first with an analytic solution to an infinite medium problem. A system of numerical equations is then formulated to be consistent with the number density iteration scheme used to simulate constant power depletion in the code REBUS at Argonne National Laboratory. A two-dimensional (R-Z) fast reactor example similar to that used by previous authors for constant flux depletion is solved here to provide a consistent basis for evaluating the present work. The sensitivity coefficients predicted by constant power depletion perturbation theory are consistently within a few percent of the exact calculation.