  In this paper, we consider the solvability problems for the fully coupled
forward-backward stochastic difference equations (FBS{\Delta}Es) on spaces
related to discrete time, finite state processes. On one hand, we provide the
necessary and sufficient condition for the solvability of the linear
FBS{\Delta}Es. On the other hand, under the assumption that the coefficients
satisfy the monotone condition, we investigate the existence and uniqueness
theorems for the general nonlinear FBS{\Delta}Es.
