An open system is a real-time system that dynamically executes independently developed real-time applications with non real-time 0 on general purpose computers. This paper focuses on the method for scheduling real-time applications in open system environment, where the real-time application is composed of different kinds of real-time tasks ; hard real-time tasks and soft real-time tasks. If the real-time application is composed of only hard real-time tasks, it was sufficient for operating system to guarantee the schedulability of tasks in runtime because the schedulability of hard real-time tasks can be validated in off-line. However, if the real-time application is composed of both of kinds of tasks, a developer can not validate the schedulability of tasks in the application. Thus, the operating system have to do ad-mission control in runtime. Once the application is admitted, the operating system have to guarantee the schedulability of each task in the application. In this paper, we propose a 5 scheduling scheme that guarantee the more fine-grained schedulability of each task in the application and a 5 admission control scheme "Lazy Admission Control" for the soft real-time tasks in runtime.