An apparatus 2 for processing data includes first execution circuitry 4, such as an out-of-order processor, and second execution circuitry 6, such as an in-order processor. The first execution circuitry 4 is of higher performance but uses more energy than the second execution circuitry 6. Control circuitry 24 switches between the first execution circuitry 4 being active and the second execution circuitry 6 being active. The control circuitry includes prediction circuitry which is configured to predict a predicted identity of a next sequence of program instructions to be executed in dependence upon a most recently executed sequence of program instructions and then in dependence upon this predicted identity to predict a predicted execution target corresponding to whether the next sequence of program instructions should be executed by the first execution circuitry or the second execution circuitry.