Processing circuitry executes hypervisor software to support the execution of multiple virtual machines on the processing circuitry. A memory system stores data for access by the processing circuitry and includes secure memory and non-secure memory . The secure memory is only accessible via a secure access request. Address translation circuitry is responsive to an access request issued by a current virtual machine specifying a virtual address, to perform an address translation process to identify a physical address in the memory, and to cause a modified access request to be issued to the memory system specifying the physical address. The hypervisor software sets a trusted virtual machine identifier if the current virtual machine is to be trusted to access the secure memory. The address translation circuitry can only cause the modified access request to be issued as a secure access request to the secure memory if the trusted identifier is set.