Software-intensive systems are often independently developed, operated, managed, and evolved. Progressively, communication networks have enabled these independent systems to interact, yielding a new kind of complex system, i.e. a system that is itself composed of systems, the so-called System-of-Systems (SoS). By its complex nature, SoS exhibits emergent behaviors. Nowadays, none of the Architecture Description Languages (ADLs), which have been developed for modeling the architectural behavior of single software-intensive systems, has the expressive power to formally describe the architectural behavior of Software-intensive SoSs. For addressing this research challenge, we propose a novel ADL, called SosADL, specially conceived for formally describing the architecture of Software-intensive SoSs. It embodies SoS architectural concepts and constructs encompassing the formal description of software architectures from both the structural and behavioral viewpoints. This paper presents SosADL focusing on the description of the architectural behavior of Software-intensive SoSs. It describes SosADL from its behavioral viewpoint enabling to specify independent systems, mediators among these systems, coalitions of mediated systems, and the architectural conditions that enforce the production of emergent SoS behaviors. It illustrates SosADL through an excerpt of a real application for architecting a Flood Monitoring and Emergency Response SoS.