The invention is used in a virtual machine monitor for a multiprocessing system that includes a virtual memory system. During a software-based processing of a guest instruction, including translating or interpreting a guest instruction, mappings between virtual addresses and physical addresses are retained in memory until processing of the guest instruction is completed. The retained mappings may be cleared after each guest instruction has been processed, or after multiple guest instructions have been processed. Information may also be stored to indicate that an attempt to map a virtual address to a physical address was not successful. The invention may be extended beyond virtual machine monitors to other systems involving the software-based processing of instructions, and beyond multiprocessing systems to other systems involving concurrent access to virtual memory management data.