A data processing apparatus has a debug state in which processing circuitry 105 executes instructions received from the debug interface 115. Control changing circuitry 135 prohibits the execution of instructions in a predefined privilege mode when in the debug state if a control parameter has a predefined value. In response to a first exception being signalled while in the debug state, where the first exception is intended to be handled at the predefined privilege mode, and further in response to the control parameter having the predefined value, signalling circuitry 115 signals a second exception to be handled at a different privilege mode from the predefined privilege mode and sets information identifying a type of the first exception. Consequently, without having to enter the prohibited (predefined) privilege mode, the debugger 110 can be made aware of the first exception that would ordinarily be handled at the predefined, i.e. prohibited privilege mode.