System-of-Systems (SoS) refer to complex, large-scale, and often critical software-intensive systems whose importance has rapidly grown over this decade. This is the case, for instance, of SoS for energy grids, multimodal traffic control, and smart cities. We find SoS in different application areas as diverse as environment, transportation, energy, healthcare, aerospace, aeronautics, and automotive. For mastering the complexity of such evolutionary software-intensive systems, it is fundamental to be able to design their software architectures for satisfying both functional and non-functional requirements. In particular, there is the need to model and enact systematic processes to design SoS software architectures. Despite this increasing necessity, most of the SoS software architectures have been still developed in an ad hoc manner. In general, there is a lack of structured processes for architecting SoS. This state-of-art hinders SoS development, in particular for critical applications. This thesis presents SOAR (General Process for Acknowledged SoS Software Architectures) that supports the modeling and enactment of architectural design processes for acknowledged SoS. Conceived to provide different levels of support according to different SoS development contexts, it comprises a high-level kernel that describes what must be done when architecting SoS and also three practices with specific activities and work products to guide how to perform architectural analysis, synthesis, and evaluation. SOAR was implemented using Essence (Kernel and Language for Software Engineering Methods), an OMG/SEMAT Standard. To validate SOAR, three surveys, a viability study, and an experiment were conducted. Results achieved in these studies indicate that SOAR positively meets the expressed need.