The time-dependent generalized perturbation theory is applied to the neutron and the nuclide fields to obtain a general perturbative formulation of the type of the Maclaurin expansion for functionals linear with the neutron or nuclide densities. Such functionals may represent, typically, activation detections or quantitative measurements of built-up or decayed higher isotopes of fuel materials. An alternative procedure is shown by which perturbation first- and higher order expansions of the neutron or nuclide density changes can also be obtained. Two simple but representative examples confirm the validity of the formulations.