Generalized Perturbation Theory (GPT) is used with the aim of proposing a perturbation method for isotopic depletion calculations. Changes in nuclide densities over time induce variations in the neutron flux and these lead to changes in reaction rates present in the evolution matrix. The proposed perturbation method treats these reaction rates as integral quantities and changes in these integral quantities as perturbations coming from changes in nuclide densities with fuel burnup. This method is applied to a subcritical system driven by an external neutron source. The results obtained by perturbation method show good agreement with the direct calculation. Considering that only a 1D problem was tested, other problems treating more energy groups and 2 or 3 spatial dimensions should be done in order to fully validate the method.