A data processing system 2 supporting interrupt handling is provided with an interrupt controller 24. The interrupt controller is responsive to save state data when interrupt processing is commenced by pre-emption of existing processing, whether that be background processing or another interrupt. If a further interrupt is required to be executed immediately after the interrupt which triggered the pre-emption, then the speed with which interrupt processing can be started is advantageously increased if that subsequent interrupt processing is performed without restoring and then resaving the original state data. The interrupts in this arrangement can be considered to be chained together without intervening save and restore operations.