A service system is a popular concept in academia and industry. At the same time, it is a challenging concept to represent, due to its recursive nature and difficulty to relate it to entities in reality. In this paper we present an ontology for modeling service systems using the SEAM systemic method. Our ontology represents an updated and minimalistic version of the existing SEAM service modeling language that puts an emphasis on the behavior. The research approach we used is the design science for information systems research and it resulted with the ontology artifact. As part of the ontology, we provide a meta-model, well-formedness rules and formalization in the Alloy language. We conclude with presenting the limitations and a brief discussion on the contribution of shifting the focus towards the behavior in service systems.