A data processing system supporting one or more virtual processing apparatuses is provided with external interrupt interface hardware 26 and virtual interface hardware 28. Hypervisor software responds to an interrupt received by the external interrupt interface hardware 26 to write data characterising that interrupt into list registers 18 of the virtual interface hardware 28. A guest operating system for the virtual machine of the virtual data processing apparatus being emulated may then read data from the virtual interface hardware 28 characterising the interrupt to be processed by that virtual machine. The virtual machine and the guest operating system interact with the virtual interface hardware 28 as if it were external interface hardware. The hypervisor software is responsible for maintaining the data within the virtual interface hardware 28 to properly reflect queued interrupts as received by the external interface 26.