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Multiprocessor systems-on-chip (MPSoC) with distributed shared memory and caches are flexible when it comes to inter-processor communication but require an efficient memory consistency and cache coherency solution. In this paper we present a novel consistency model, streaming consistency, for the streaming domain in which tasks communicate through circular buffers. The model allows more reordering than release consistency and, among other optimizations, enables an efficient software cache coherency solution and posted writes. We also present a software cache coherency implementation and discuss a software circular buffer administration that does not need an atomic read-modify-write instruction. A small experiment demonstrates the potential performance increase of posted writes in MPSoCs with high communication latencies.