Multi-agent systems paradigm is the most appropriate one to developing complex systems. Consequently, it is used to develop real-time intelligent systems which are one of complex systems categories. In the literature, several works have been proposed for formalizing many aspects of multi-agent systems. However, the application of formal methods upon real-time multi-agent systems (RTMAS) (where the time is the primordial aspect) stills in the immaturity stage. In this paper, we present the formalization of SIMBA real-time multi-agent systems using Real-Time Maude language as a main stone for formal development of based-SIMBA systems.