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The completeness of event logs and long-distance dependencies are two major challenges for process mining. Until now, most process mining methods have not been able to discover long-distance dependency and assume that the directly-follows relationship in the log is complete. However, due to the existence of high concurrency and the cycle, it is difficult to guarantee that the real-life log is complete regarding the directly-follows relationship. Therefore, process mining needs to be able to deal with incompleteness. In this paper, we propose a method for discovering process models including sequential, exclusive, concurrent, and cyclic structures from incomplete event logs. The method analyzes the co-occurrence class of the log and the model and then uses the technology of combining the behavior profile and co-occurrence class to obtain the communication behavior profile of the co-occurrence class. Furthermore, a method of constructing a substructure from the event log using the co-occurrence class is presented. Finally, the whole process model is built by combining those substructures. The experimental results show that the proposed method can discover process models with complex structures involving cycles from incomplete event logs and also can deal with long-distance dependency in the event log. Meanwhile, the discovered process model has a good degree of consistency with the original model. [ABSTRACT FROM AUTHOR]