Packet-processing circuitry including one or more flow caches whose contents are managed using a cache-entry replacement policy that is implemented based on one or more updatable counters maintained for each of the cache entries. In an example embodiment, the implemented policy enables the flow cache to effectively catch and keep elephant flows by giving to the caught elephant flows appropriate preference in terms of the cache dwell time, which can beneficially improve the overall cache-hit ratio and/or packet-processing throughput. Some embodiments can be used to implement an Open Virtual Switch (OVS). Some embodiments are advantageously capable of implementing the cache-entry replacement policy with very limited additional memory allocation.