  We show that quantum optical systems preserving the total number of
excitations admit a simple classification of possible resonant transitions
(including effective), which can be classified by analizying the free
Hamiltonian and the corresponding integrals of motion. Quantum systems not
preserving the total number of excitations do not admit such a simple
classification, so that an explicit form of the effective Hamiltonian is needed
to specify the allowed resonances. The structure of the resonant transitions
essentially depends on the algebraic propereties of interacting subsystems.
