  We study the time evolution of quantum systems with a time-dependent
non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2)
generators.With a time-dependent metric, the pseudo-Hermitian invariant
operator is constructed in the same manner as for both the SU(1,1) and SU(2)
systems. The exact common solutions of the Schr\"odinger equations for both the
SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the
pseudo-Hermitian invariant operator.
