Compatibility of components is an important issue in the quest for systems of systems that guarantee successful communications, free from message loss and indefinite waiting for inputs. In this paper, we investigate compatibility in the context of systems consisting of reactive components which may communicate through the synchronised execution of common actions. We model such systems in the team automata framework, which does not impose any a priori restrictions on the synchronisation policy followed to combine the components. We identify a family of representative synchronisation types based on the number of sending and receiving components participating in synchronisations. Then, we provide a generic procedure to derive, for each synchronisation type, requirements for receptiveness and for responsiveness of team automata that prevent that outputs are not accepted and inputs are not provided, respectively. Due to the genericity of our approach w.r.t. synchronisation policies, we can capture compatibility notions for various multi-component system models known from the literature.