Each of plural processing units has a cache, and each cache has indication circuitry containing segment filtering data. The indication circuitry responds to an address specified by an access request from an associated processing unit to reference the segment filtering data to indicate whether the data is either definitely not stored or is potentially stored in that segment. Cache coherency circuitry ensures that data accessed by each processing unit is up-to-date and has snoop indication circuitry whose content is derived from the already-provided segment filtering data. For certain access requests, the cache coherency circuitry initiates a coherency operation during which the snoop indication circuitry determines whether any of the caches requires a snoop operation. For each cache that does, the cache coherency circuitry issues a notification to that cache identifying the snoop operation to be performed.