A set of local invalidation buses for a highly scalable shared cache memory hierarchy is disclosed. A symmetric multiprocessor data processing system includes multiple processing units. Each of the processing units is associated with a level one cache memory. All the level one cache memories are associated with an imprecisely inclusive level two cache memory. In addition, a group of local invalidation buses is connected between all the level one cache memories and the level two cache memory. The imprecisely inclusive level two cache memory includes a tracking means for imprecisely tracking cache line inclusivity of the level one cache memories. Thus, the level two cache memory does not have dedicated inclusivity bits for tracking the cache line inclusivity of each of the associated level one cache memories. The tracking means includes a last_processor_to_store field and a more_than_two_loads field per cache line. When the more_than_two_loads field is asserted, except for a specific cache line in the level one cache memory associated with the processor indicated in the last_processor_to_store field, all cache lines within the level one cache memories that shared identical information with that specific cache line are invalidated via the local invalidation buses connected between all the level one cache memories and the level two cache memory.