ProCom is a new component model for real-time and embedded systems, targeting the domains of vehicular and telecommunication systems. In this paper, we describe how the architectural elements of the ProCom component model have been given a formal semantics. The semantics is given in a small but powerful finite state machine formalism,with notions of urgency, timing, and priorities. By defining the semantics in this way, we (i) provide a rigorous and compact description of the modeling elements of ProCom, (ii) seethe ground for formal analysis using other formalisms, and(iii) provide an intuitive and useful description for both practitioners and researchers. To illustrate the approach,we exemplify with a number of particularly interesting cases, ranging from ports and services to components and component hierarchies.