Wormhole routing networks have become increasingly popular for low latency, highspeed interconnection of supercomputer and workstation clusters. An example is the Supercomputer SuperNet (SSN) at UCLA, which interconnets supercomputer across campus and metropolitan area distances. SSN employs a two-level network architecture in which an optical backbone network interconnets several high- speed, wormhole-routing local area networks (Myrinets). SSN applications such a scientific visualization and rendering require that the networks support reliable delivery of traffic characterized by Quality of Service (QoS) parameters. Motivated by this requirement, we investigate QoS support in Myrinet-like high- speed, wormhole routing networks. Since native Myrinet protocols do not provide QoS support, we explore several novel strategies including (a) the use of a separate subnet for carrying such traffic (along with source pacing), (b) the overlay of a virtual synchronous system on the asynchronous network, and (c) the introduction of virtual channels. We discuss the tradeoffs among the different options and evaluate them via selected simulation experiments.