We study the lateral transport of two-dimensional randomly layered med
ia in the presence of isotropic randomness. The hopping anisotropy is
also included. Equilibration length and channel occupation number are
calculated by using both the recursive Green's-function method and the
rate-equation approach. Our results show clearly a transition from er
godic to nonergodic transport as the number of layers increases. This
describes a dimensional-crossover behavior from two-dimensional-like a
nisotropic hopping systems to one-dimensional-like randomly layered me
dia.