Replay of shared memory program execution is desirable in many domains including cyclic debugging, fault tolerance and perfom,ance monitoring. Past approaches to repeatable execution have focused on the problem of re-executing the shared memory access patterns in parallel programs. With the proliferation of operating system supported threads and shared memory for uniprocessor programs, there is a clear need for efficient replay of concurrent applications. The solutions for parallel systems can be performance prohibitive when applied to the uniprocessor case. We present an algorithm, called the repeatable scheduling algorithm, combining scheduling and instruction counts to provide an invariant for efficient, language independent replay of concurrent shared memory applications. The approach is shown to have trace overheads that are independent of the amount of sharing that takes place. An implementation for cyclic debugging on Mach 3.0 is evaluated. The algorithm implemented is compared with optimal event-based tracing and shown to do better with respect to the number of events monitored or number of events logged, in some cases by several orders of magnitude.