A critical issue for the design of a System-of-Systems (SoS) is the formal description of its architecture. One of the complicating factors for formally describing SoS architectures is that they evolve dynamically, during run-time, in unexpected ways. Today, none of the existing process calculi applied for formally describing the architecture of software-intensive single systems has the expressive power to formally describe the architecture of software-intensive SoSs. To address this issue, this paper proposes a novel process calculus, the π-Calculus for SoS, which was specially conceived for enabling the formal architecture description of software-intensive SoSs, meeting their challenging characteristics.