A computer system including a processor and memory, the processor having a virtual mode of operation in which it uses a virtual machine monitor which allows it to service a plurality of users contemporaneously in a multiplexed manner, and a non-virtual, or real, mode of operation. The computer system has a set of at least three operation mode protection rings representing a hierarchy of access privilege levels in both the real and virtual modes, with the number of privilege levels in both the real and virtual modes being the same. The privilege levels govern the accessibility of memory locations to programs and the executability of certain privileged instructions, which cause control to be transferred to the virtual machine monitor when the processor is in a virtual mode. The two most privileged levels in the virtual mode are both treated as corresponding to the second most privileged level in the real mode, whereby if the processor is in the most privileged virtual operating mode, access to memory locations is permitted only if the location is accessible to the second most privileged mode. When an instruction is retrieved, the processor first performs a probe operation to determine whether it can access any required memory locations in response to its current privilege level, and then determines whether it is in a privilege level which allows it to process the instruction.