  We investigate low-energy properties of two-dimensional quantum spin systems
with the ladder and plaquette structures, which are described by a generalized
antiferromagnetic Heisenberg model with both of the bond and spin alternations.
By exploiting a non-linear $\sigma$ model technique and a modified spin wave
approach, we evaluate the spin gap and the spontaneous magnetization to discuss
the quantum phase transition between the ordered and disordered states. We
argue how the spin-gapped phase is driven to the antiferromagnetic phase in the
phase diagram.
