For automatically composing Web services in a correct manner, information about their behaviors (an abstract model) has to be published in a repository. This abstract model must be sufficient to decide whether two, or more, services are compatible (the composition is possible) is possible without including any additional information that can be used to disclose the privacy of these services. The compatibility between two Web services can be based either on some generic properties (e.g. deadlock freeness of the composite Web service) or on a specific property expressed with a formal logic. In this paper, the authors address this problem by considering these two kinds of compatibility criteria. The first criterion is defined by different variants of the well-known soundness property on open workflow nets. These properties guarantee the absence of livelocks, deadlocks and other anomalies that can be formulated without domain knowledge. The second criterion is defined by the designer formally by using the Linear Temporal Logic. The proposed approach addresses the automatic abstraction of Web services and the checking of their compatibility using their abstract models only. To abstract Web services, the authors use the symbolic observation graph (SOG) approach that preserves necessary information for service composition and hides private information. The authors show how the SOG can be adapted and used so that the verification of generic and specific compatibility criteria can be performed on the composition of the abstract models of Web services instead of the original composite service.