A hardware transactional memory 12, 14, 16, 18, 20 is provided within a multiprocessor 4, 6, 8, 10 system with coherency control and hardware transaction memory control circuitry 22 that serves to at least partially manage the scheduling of processing transactions in dependence upon conflict data 26, 28, 30. The conflict data characterises previously encountered conflicts between processing transactions. The scheduling is performed such that a candidate processing transaction will not be scheduled if the conflict data indicates that one of the already running processing transactions has previously conflicted with the candidate processing transaction.