  We analyse periodically modulated quantum systems with $SU(2)$ and $SU(1,1)$
symmetries. Transforming the Hamiltonian into the Floquet representation we
apply the Lie transformation method, which allows us to classify all effective
resonant transitions emerging in time-dependent systems. In the case of a
single periodically perturbed system, we propose an explicit iterative
procedure for the determination of the effective interaction constants
corresponding to every resonance both for weak and strong modulation. For
coupled quantum systems we determine the efficient resonant transitions
appearing as a result of time modulation and intrinsic non-linearities.
