Some issues of scheduling tasks with precedence constraints and shared resource are discussed in this paper. The authors present the scheduling algorithm QNES ( quasi-normality－EDF－scheduler) by means of defining the notion of quasi- normality and making consistency of precedence constraints among tasks and parti al order on tasks. QNES can access shared resource based on PCP (priority ceilin g protocol) or SRP (stack resource policy) protocols, and has characters of preemption, dealing with precedence constraints among tasks and accessing sh ared resource, and is suitable to uni-processor systems.