With the rise of data-centric process management paradigms, interdependent processes, such as artifacts or object lifecycles, form a business process through their interactions. Coordination processes may be used to coordinate these interactions, guiding the overall business process towards a meaningful goal. A coordination process model specifies coordination constraints between the interdependent processes in terms of semantic relationships. At run-time, these coordination constraints must be enforced by a coordination process instance. As the coordination of multiple interdependent processes is a complex endeavor, several challenges need to be fulfilled to achieve optimal process coordination. For example, processes must be allowed to run asynchronously and concurrently, taking their complex relations into account. This paper contributes the operational semantics of coordination processes, which enforces the coordination constraints at run-time. Coordination processes form complex structures to adequately represent processes and their relations, specifically supporting many-to-many relationships. Based on these complex structures, markings and process rules allow for the flexible enactment of the interdependent processes while fulfilling all challenges. Coordination processes represent a sophisticated solution to the complex problem of coordinating interdependent, concurrently running processes.