Recently, there has been recognized a significant movement towards services, which is reflected in GDP of countries as well as it is mirrored by customers needs and expectations. Therefore, since the services are provided by means of service systems, the attention has to be paid to the service systems and their description. The Service Science theory is being developed and improved every day, hence it will take some time to build it stabile and sound. Basic and commonly shared knowledge is still missing.
This paper contributes to the service science foundation. Based on extended definition of service systems, it proposes the concept of a prime service system as a service system in a context of clients benefits. A definition of the cooperation of service systems is given and the paper concludes with a definition of a dual service system, which is a service system based on collaboration of two prime service systems. The paper discusses the introduced concepts on examples of business enterprises and academic institutions.