A system whereby a central processor continues operation beyond a serialization point before the architecture defines that it is permissible to do so. According to the system, it is ascertained whether correct results are being achieved after the serializing point. If some doubt develops about the correctness of the results, the processor is returned to its status at the serialization point and the processing is repeated. In one embodiment, correctness of results is determined by way of a monitoring mechanism which depends on the fact that interactions between CPUs are confined to references to storage. The operations which are performed prior to the time that the architecture allows them, are restricted to ones which depend on fetches made from storage. The needed assurance of correct operation is gained by monitoring the storage locations from which fetches are made on behalf of instructions which logically follow the serializing operation, but which are made prior to the time that fetching is allowed to resume. If those storage locations are not changed during the time between when the first such fetch is actually made from one of them, and the time that fetching is allowed to resume, then the results of the processing which was done by the CPU (based on those fetches) must be exactly the same as if all of the fetches and processing was done in a single instant at the moment that the fetches became allowed.