1. An apparatus comprising: processing circuitry to execute program instructions including a transaction comprising a number of program instructions that execute to generate updates to state data and to commit said updates if said transaction completes without a conflict; and control storage to store stepping control data used to control operation of the processing circuitry; the processing circuitry being responsive to the stepping control data having a first value to operate in a single stepping mode, where the processing circuitry initiates a debug event following execution of each instruction; the processing circuitry being responsive to the stepping control data having a second value to operate in a step over transaction mode, where the processing circuitry is arranged, when executing the number of program instructions within the transaction, to suppress initiation of the debug event until the transaction has completed.