Abstract: A memory manager for a virtual memory system maintains three lists of virtual addresses: those which are free to be mapped to a program, those which are currently mapped but no longer being used, and those which are being removed from a page table, i.e. unmapped. The allocation of free addresses to programs proceeds in parallel with the removal of old entries from the page table, such that new free addresses are guaranteed to be available at all times. Each time that a new address is allocated to a program, a limited number of entries in the page table are examined, to determine whether the addresses associated with those entries are no longer in use, and the entries can be removed from the page table. By the time that all of the available addresses in the free list have been allocated, the entire page table will have been examined and all addresses which are no longer in use will have had their corresponding page table entries removed, so that they are available as free addresses.