The present invention discloses a method and apparatus that uses extensions to the TLB entry to dynamically identify pages of memory that can be weakly ordered or must be strongly ordered and enforces the appropriate memory model on those pages of memory. Such identification and memory model enforcement allows for more efficient execution of memory instructions in a hierarchical memory design in cases where memory instructions can be executed out of order. From the page table, the memory manager constructs TLB entries that associate page frame numbers of memory operands with page-granular client usage data and a memory order tag. The memory order tag identifies the memory model that is currently being enforced for the associated page of memory. The memory manager updates the memory order tag of the TLB entry in accordance with changes in the client usage information. In the preferred embodiment, the TLB structure is a global TLB shared by all processors. In alternative embodiments, the TLB structure may comprise either multiple distributed TLBs with shared knowledge, each assigned to a different processor, or a combination of multiple local TLBs, each assigned to a different processor, that exchange information with a global TLB, which in turn provides data to the memory manager to access the hierarchical memory system.