A hardware and/or software facility for controlling the order of operations performed by threads of a multithreaded application on a multiprocessing system is provided. The facility may serialize or selectively-serialize execution of the multithreaded application such that, given the same input to the multithreaded application, the multiprocessing system deterministically interleaves operations, thereby producing the same output each time the multithreaded application is executed. The facility divides the execution of the multithreaded application code into two or more quantum specifying a deterministic number of operations, and the facility specifies a deterministic order in which the threads execute the two or more quantum. The facility may operate together with a transactional memory system. When the facility operates together with a transactional memory system, each quantum is encapsulated in a transaction that, may be executed concurrently with other transactions, and is committed according to the specified deterministic order.