On building a service-oriented architecture for grid systems, more and more researches have been focused on service composition. Services, however, are not always exactly compatible and much effort has to be addressed to mediate incompatible services, which is an unavoidable problem and recognized as service composition mismatches. To address it, a classification of composition mismatches is significant and helpful to divide the whole problem into different sub-problems which require corresponding mediators to deal with. However, there exist very few classification approaches specific to such problem and a comprehensive classification is still lacking. In this paper, a classification of most kinds of composition mismatches is introduced. Besides that, several basic protocol mismatch patterns are presented, which can be viewed as basic constructs of existing protocol mismatches. Finally, conclusions and the future work are drawn up.