A system, method and computer program product for processing overflow transactions in a transactional memory system. The transactional memory system is provided in a multiprocessing system having one or more processor devices and a shared memory storage system, and implements a best effort hardware transactional memory system. The method includes acquiring, by a requesting processor, lockbits associated with a memory structure of the shared memory storage system to be reserved for an overflowing transaction. The lockbits determine the granularity at which memory reservations for an overflow transaction are recorded. The method includes implementation of control mechanism for controlling concurrency between overflowing and non-overflowing transactions requested by processor devices in the multiprocessing system, the method enabling only one overflowing transaction to execute at a time in the multiprocessing system.