In this thesis, the Goal Process model which is a new parallel execution model of Prolog programs and X-WAM multiprocessor System(X-WAMS) are proposed. The Goal Process Model supports restricted AND parallelism with both intelligent back-tracking and eager OR. Compared to the other models for AND parallel execution of Prolog programs, the Goal Process Model can enhance the performance of nondeterministic programs with a lot of backtrackings due to both the eager OR and the intelligent backtracking. As an intermediate code for the Goal Process Model, extended conditional graph expression which is an extension of the conditional graph expression of DeGroot is also suggested. The extended conditional graph expression contains the information for both the forward execution and the backward execution of a clause. It is generated automatically by a static flow analysis of a given program. The X-WAMS is a multiprocessor system which can support both AND and OR parallelism. The control mechanism of the X-WAMS is based on the Goal Process Model. However, OR parallelism can also be exploited in the X-WAMS by the static split of a Prolog program. That is, after a given program is split into disjoint programs for OR parallel execution, they are distributed over all the processors in the X-WAMS. Then, a disjoint program is solved independently by a processor using the control mechanism of the Goal Process Model., Therefore, the static decision for OR parallel execution and the dynamic decision for AND parallel execution are made in the X-WAMS.