A memory system for association with a user processor for operation independently from the user processor includes a physical memory and an interface unit for enabling the associated user processor to access the physical memory. The physical memory is represented in a virtual address space which is garbage collected in parallel with the operation of the user processor. The garbage collection process includes reference count deallocation and a garbage collection algorithm for deallocating cyclic structures not deallocated by the reference count process. The reference count process includes providing for a reference count indicating the number of pointer references to a memory block in the virtual address space. When the reference count becomes zero, and no other references to a memory block exist, the block may be freed. In the garbage collection algorithm, the virtual memory space is traced in areas, called OLDSPACE, and compactly copied into a new area, called NEWSPACE. The OLDSPACE and NEWSPACE are further scavenged to insure that all referenced blocks of memory are copied, and the remaining OLDSPACE is cleaned. The garbage collection process is performed in parallel with the operation of the user processor.