A new quasidegenerate perturbation theory is developed that describes the interactions of electronic states of interest with energetically low-lying excited states variationally and with more high-lying excited states perturbatively. The states of interest, the low-lying excited states and the more high-lying excited states, define primary, secondary, and external subspaces, respectively. The task of determination of the lowest solutions of the full configuration interaction (CI) problem is shown to be equivalent to the task of searching iteratively for an optimal primary subspace within the model space spanned by the initial unperturbed primary and secondary states. It is also shown that the present approach, which we refer to as the self-consistent quasidegenerate perturbation theory (SC-QDPT), theoretically satisfies the following criteria: (1) it avoids instabilities due to intruder states; (2) it ensures the additivity of the energy for noninteracting subsystems; (3) the projection of the correlated wave functions on the model space coincides with the optimal primary subspace; and (4) the energies of the primary states will be restricted below by the full CI limit. Furthermore, by use of an exponential ansatz the model space effective Hamiltonian takes into account finite-order primary-external perturbations exactly. Some of these conclusions are corroborated by the results of application of the lowest-order approximation, SC-QDPT(SD), of the method on the beryllium atom and on the reaction Be+H-2, using a simple computer realization.