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Network-on-chip (NoC) designs have emerged as a replacement for traditional shared-bus designs for on-chip communication. As with all current very large scale integration designs, however, reducing power consumption in NoCs is a critical challenge. One approach to reduce power consumption is to dynamically scale the voltage and frequency of each network node or groups of nodes (DVFS). Another approach is to replace the balanced clock tree with a globally-asynchronous, locally-synchronous (GALS) clocking scheme. In both DVFS and GALS designs, the chip as a whole is multi-synchronous. As the NoCs interconnecting those nodes must communicate across these clock domain boundaries, they tend to have high latencies as packets must be synchronized at the intermediate nodes. In this paper, we propose a novel router microarchitecture which offers superior performance with respect to typical synchronizing router designs for multi-synchronous networks. Our approach features asynchronous bypass channels which allow flit traversal of intermediate nodes within the network without the latching or synchronization overheads of typical designs. We also propose a new network topology and routing algorithm that leverage the advantages of the bypass channel offered by our router design. We present a detailed analysis of design decisions which affect the performance of the asynchronous bypass channel network. Our experiments show that our design improves the performance of a conventional synchronizing design with similar resources by up to 26% at low loads and increases saturation throughput by up to 50% for a uniform random traffic.