Wormhole routing networks have become increasingly popular for low latency, high-speed interconnection of supercomputer and workstation clusters. An example is the Supercomputer SuperNet (SSN) at UCLA, which interconnects supercomputers across campus and metropolitan area distances. SSN employs a two-level network architecture in which an optical backbone network interconnects several high-speed, wormhole-routing local area networks (Myrinets). SSN applications such as scientific visualization and rendering require that the network 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 these networks do not provide QoS support, we explore several novel strategies including (a) the use of a separate subnet for carrying such traffic (along with the use of pacing), (b) superimposing a virtual synchronous system on the asynchronous network, and (c) employing virtual channels to provide QoS support while integrating QoS traffic and non-QoS (or datagram) traffic on the same network. We discuss the tradeoffs among the different options and evaluate them via selected simulation experiments.