This paper presents scheduling and admission control algorithms for access to processor and storage resources of a video file server. The scheduling algorithms support multiple classes of tasks with diverse performance requirements, allow for the co-existence of guaranteed real-time requests with sporadic, and unsolicited requests, and ensure system stability during overloads. Performance guarantees are maintained for real-time streams in the presence of unpredictably varying non real-time traffic. A prototype video file server was implemented on an Intel 486 platform. Performance results show that a large number of streams can be supported, while maintaining efficient utilization of system resources.