A variational theory is developed for estimating reactivity worths (and other bilinear ratios) and reaction rate ratios in critical nuclear reactors. These estimates embody corrections to first-order perturbation theory which account for the flux change caused by the reactivity perturbation and for the changes in the flux and adjoint when the system is altered. The physical significance of certain generalized functions which arise in the development of the theory is investigated. The relation of the variational theory to generalized perturbation theory is examined, and the additional restrictions required to reduce the former to the latter are established. Finally, the variational theory is demonstrated to yield accurate estimates for reactivity worths and reaction rate ratios in a fast reactor model, subject to a wide range of alterations in nuclear properties and compositions.