A data processing apparatus (2) has a number of devices (4) having a normal state and a quiescent state. Transition sequencing circuitry (70) controls a sequential state transition process for transitioning each of the devices (4) in turn between the normal state and the quiescent state. For each device, the transition sequencing circuitry (70) controls the transition based on at least one preference indication transmitted from that device (4) providing an indication of a preference to operating the normal state or the quiescent state.