Web services can be viewed as processes of an enterprise which are used by (processes of) other enterprises. So, when offering a web service, it is necessary to publish sufficient information about the interface of the web service process. On the other hand, details of the internal behaviour of a web service should be hidden. So the design of complex inter-enterprise business processes(IEBP) employing web services is generally performed in a modular way. Each service is designed separately from the others and then the whole IEBP is obtained by composition. Even if such a modular approach is intuitive and facilitates the design problem, it poses the problem that correct behavior of each service of the IEBP taken alone does not guarantee a correct behavior of the composed IEBP (i.e. properties are not preserved by composition). In this paper, we address this problem. First, we propose to use a new variant of symbolic observation graphs as an abstraction of any service of the IEBP (only cooperative activities are visible). Local deadlock freeness can be checked efficiently on such an abstraction using symbolic algorithms. Second, we propose to synchronize the symbolic observation graphs associated with the different processes of the IEBP and supply an efficient algorithm for the verification of deadlock freeness of the synchronized product. The deadlock freeness of such a product guarantees a correct possible cooperation between the underlying processes (i.e. a deadlock free cooperation).