Depletion perturbation theory has been extended to the closed nuclear fuel cycle, and methods have been developed for computing the constrained sensitivities that account for fuel reprocessing and fabrication. An iterative method was developed to solve the sensitivity equations and applied to the closed fuel cycle of the Integral Fast Reactor (IFR). The sensitivities computed using the method were in good agreement with sensitivities from direct subtraction of perturbed and unperturbed depletion calculations. The closed fuel cycle sensitivities were also compared with the sensitivities for the open fuel cycle without reprocessing. The closed fuel cycle sensitivities were found to be larger, particularly for isotopes higher up the burnup chain. These results indicate this work would have particular importance for the analysis of advanced reactor designs with closed fuel cycles, such as the IFR. The methods developed here will facilitate accurate and efficient sensitivity studies of such reactors.