The article presents an algebraic approach to process cooperation, focusing on four key cases: free merge, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. It introduces an equational specification of process cooperation and shows that the rewrite system behind the communication algebra is confluent and terminating modulo permutative reductions. The paper also explores relationships between the four merging concepts. The authors propose an algebra of processes based on elementary actions and operators + (choice), · (product), and | (merge). An auxiliary operator, ⊓, is introduced to simplify computations and enhance expressive power. The paper discusses the axiom systems PA (for free merge), ACP (for communication), AMP (for mutual exclusion of tight regions), and ASP (for synchronous cooperation). It also compares these systems with related approaches like Milner's CCS and the dot calculus. The paper establishes mathematical properties of these systems, including consistency and a normal form theorem for process expressions. It also discusses the relationship between ACP and CCS, and notes that ACP does not address the problem of hiding or abstraction in processes. The paper concludes with a discussion of the broader implications of these findings for the study of concurrency and process algebra.The article presents an algebraic approach to process cooperation, focusing on four key cases: free merge, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. It introduces an equational specification of process cooperation and shows that the rewrite system behind the communication algebra is confluent and terminating modulo permutative reductions. The paper also explores relationships between the four merging concepts. The authors propose an algebra of processes based on elementary actions and operators + (choice), · (product), and | (merge). An auxiliary operator, ⊓, is introduced to simplify computations and enhance expressive power. The paper discusses the axiom systems PA (for free merge), ACP (for communication), AMP (for mutual exclusion of tight regions), and ASP (for synchronous cooperation). It also compares these systems with related approaches like Milner's CCS and the dot calculus. The paper establishes mathematical properties of these systems, including consistency and a normal form theorem for process expressions. It also discusses the relationship between ACP and CCS, and notes that ACP does not address the problem of hiding or abstraction in processes. The paper concludes with a discussion of the broader implications of these findings for the study of concurrency and process algebra.