The goal of this investigation is to demonstrate the application of a process modelling approach to architect a System of Systems (SoS) capable of conducting Anti-Submarine Warfare (ASW) operations projecting to the year 2025. Process modelling is a methodology for architectural analysis for complex systems whose operation is characterised by ‘processes’ whose sequential execution may be scaled-up to understand overall system behaviour. It is ideally suited to address complexity and interoperability issues of an ASW SoS. New contributions of this work include the successful implementation of a process modelling approach to architect an ASW SoS and a cohesive set of results analysing its operation with future projections to the year 2025. We believe this work may serve as a foundation for future systems engineering research addressing interoperability and performance of complex systems whose function is closely tied to time-dependent processes, with particular application to military and security systems.