We present a time domain extension of the hierarchical and modular discrete event specification(DEVS) formalism. This extension is important for establishing a seamless real-time software development framework. Formalisms help describe a system unambiguously. If formal models are implemented without any consistent frameworks, however, it is hard to guarantee that there is no semantic gap between models and codes. Real-Time DEVS, named RTDEVS, is an extension of DEVS that can be characterized in three perspectives: the real time execution of models, the addition of time interval functions, and the activity specification for each state. After analyzing a system, the framework based on RTDEVS helps to expand each model of the system for executing in a real-time environment. In order to support the RTDEVS formalism, we propose abstract executive concepts based on the abstract simulator concepts of the DEVS formalism. Also, we implement an RTDEVS execution engine, named DEVS Executive, which runs on real-time Mach.