A formalism is developed for calculating Berry phases for non-adiabati
c time-periodic quantum systems when a dynamical invariant is known. I
t is found that, when the invariant is periodic and has a non-degenera
te spectrum, this method allows a convenient way to obtain generalized
Berry phases and the proper cyclic initial states. The method is appl
ied to the generalized harmonic oscillator and the two-level system, w
here the invariant operators are explicitly constructed. Formulae for
the conventional Berry's phases are readily obtained by taking the adi
abatic limit of the exact results.