The goal of this paper is to obtain a better understanding of the issues involved in selecting and implementing a memory consistency condition. The authors give a formal and precise definition of hybrid consistency, which is a mixed consistency condition for shared-memory multiprocessors. They present a completely asynchronous algorithm that implements hybrid consistency on distributed-memory machines. The correctness and performance of this algorithm are analyzed. The response time of the algorithm is proven to be a constant multiplicative factor of the optimal time. The authors also derive lower bounds on the response time of any implementation of hybrid consistency. This valuable research report is intended for researchers working on the theory of distributed computation.