We offer a new iterative method for exciton theory and develop a theory of exciton states arising in a plane resonant-tunnelling nanostructure based on semiconducting nitrides. Our approach takes into account the contributions of internal electric fields arising in its layers and employs both iterative and variational methods. We compare our method with the other techniques known in the exciton theory on example of a nanosystem representing a separate cascade of quantum cascade detector, which has been earlier implemented experimentally. The electron and hole spectra, the spectra of excitons and their binding energies, as well as the intensities of electron–hole transitions are calculated as functions of geometric parameters of the nanostructure. Particular cases of light-hole and heavy-hole excitons are analyzed.