Several multiprocessor computer systems, each having its own copy of an operating system, are interconnected to form a multi-computer system having global memory accessible by any processor on any node and including provision for spinlock access control. In this environment, a global mutex, and other like synchronization objects, are realized that can control the coordination of multiple threads running on multiple processors and on multiple nodes or platforms. Each global mutex is supported by a local operating system shadow mutex on each node or platform where threads have opened access to the global mutex. Global mutex functionality is thus achieved that reflects and utilizes the local operating system's mutex system.