We present a triangle ordering mechanism that maintains triangle ordering of coherence messages in SMP systems. If cache A sends a multicast message to caches B and C, and if cache B sends a message to cache C after receiving and processing the multicast message from cache A, the triangle ordering mechanism ensures that cache C processes the multicast message from cache A before processing the message from cache B. The triangle ordering mechanism enables efficient snoopy cache coherence in SMP systems in which caches communicate with each other via message-passing networks. A modified version of the triangle ordering mechanism categorizes coherence messages into non-overlapping sequencing classes, and ensures triangle ordering for coherence messages in the same sequencing class. The modified triangle ordering mechanism can significantly reduce potential performance degradation due to false waiting.