Responsive Multithreaded (RMT) Processor that controls thread execution in Simultaneous Multithreading by introducing thread priority has been invented for parallel and distributed real-time processing. This paper concerns the basic approach of real-time scheduler on RMT processor. Our goal is to build a system where various types of tasks reside; hard/soft real-time tasks, periodic/aperiodic tasks and so on. We mainly focus on the point of periodic task scheduling and aperiodic task scheduling with making use of hardware supports. Our approaches in this paper are based on the extension of the existing approaches for RMT processor as the algorithm EDF-FF and the deferrable server. The performance evaluation shows the effectiveness of our approach on RMT processor in the sense of deadline miss ratio and response time.