Monitoring apparatus is provided to allow out-of-sequence fetching of operands while preserving the appearance of in-sequence fetching to the processor of a computer. The key elements include a stack (119) of N entries holding the addresses of the last M, where M is less than or equal to N, out-of-sequence fetches. A comparator (103) is provided for comparing addresses in the stack with a test address. This test address is supplied via an OR gate (107) as either store addresses or cross-invalidate addresses, the latter being for a multiprocessor system. The addresses in the stack that compare with the test address are set as invalid. In addition, all addresses in the stack are set as invalid on the occurrence of a cache miss or serializing instruction. Finally, a select and check entry function (113) associates an address in the stack with the instruction it represents and deletes the address from the stack when the instruction is handled in its proper sequence.