Disclosed is a symmetric multiprocessor data processing system (SMP) that implements a TLBI protocol, which enables multiple TLBI operations from multiple processors within a partition to complete concurrently. Thus, a global TLB lock, synchronization, and TLB unlock is not necessary. When a TLBI instruction is executed, the master dynamically manages the behavior of the TLBI operation based on asynchronously snooping another TLBI. If concurrent TLBI management is required, then the master dynamically degrades the TLBI to a “barrier” class instruction.