A message driven architecture for the execution of OR-parallel logic languages is proposed. The computational model is based on well known compilation techniques for Logic Languages. We present first the multiple binding mechanism for the OR-parallel Prolog architecture and the corresponding OR-parallel abstract machine is described. A scheduling algorithm which does not rely upon the availability of global data structures to direct the search for work is discussed. The message driven processor, the processing node of the parallel machine, is designed to interact with a shared global address space and to efficiently process messages from other processing nodes. We discuss some of the results obtained from a high level functional simulator of the message driven machine.