The advent of multimedia ushers forth a growing class of applications that must manipulate digital audio and video within well-defined timeliness requirements. Existing processor schedulers are inadequate in supporting these requirements. They fail to allow the integration of these continuous media computations with conventional interactive and batch activities. We have created a new scheduler that provides integrated processor scheduling for all classes of computational activities. Our solution achieves optimal performance when all timeliness requirements can be satisfied, and provides graceful degradation when the system is overloaded. Though unique in the degree to which it allows users control over the dynamic sharing of processing resources, the scheduler does not impose any draconian demands on the user to provide information he does not have or does not choose to specify.