This paper presents an equational specification of process cooperation within an algebraic theory of processes. It considers four cases of process merging: free merge (interleaving), merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The authors introduce an auxiliary operator, L (left-merge), which simplifies computations and enhances the expressive power of the system. They define an algebra of processes based on elementary actions and operators + (alternative composition), · (sequential composition), and || (parallel composition). The system ACP, which includes operators for communication and encapsulation, is shown to be a finite axiomatisation of its intended models. ACP is closely related to Milner's CCS, but differs in several key aspects, such as the absence of certain operators and the inclusion of encapsulation. The paper also discusses the relationships between the four merging concepts and provides a detailed analysis of the algebraic properties of the systems. The authors show that the rewrite system behind the communication algebra is confluent and terminating, and that the systems ACP and ACMP are consistent and conservative extensions of their respective bases. The paper concludes with a discussion of the applications of these systems in the context of process algebra.This paper presents an equational specification of process cooperation within an algebraic theory of processes. It considers four cases of process merging: free merge (interleaving), merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The authors introduce an auxiliary operator, L (left-merge), which simplifies computations and enhances the expressive power of the system. They define an algebra of processes based on elementary actions and operators + (alternative composition), · (sequential composition), and || (parallel composition). The system ACP, which includes operators for communication and encapsulation, is shown to be a finite axiomatisation of its intended models. ACP is closely related to Milner's CCS, but differs in several key aspects, such as the absence of certain operators and the inclusion of encapsulation. The paper also discusses the relationships between the four merging concepts and provides a detailed analysis of the algebraic properties of the systems. The authors show that the rewrite system behind the communication algebra is confluent and terminating, and that the systems ACP and ACMP are consistent and conservative extensions of their respective bases. The paper concludes with a discussion of the applications of these systems in the context of process algebra.