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Frequent co-changes to multiple files, i.e., evolutionary coupling, can demonstrate active relations among files, explicit or implicit. Although evolutionary coupling has been used to analyze software quality, there is no systematic study on the categorization of frequent co-changes between files which may used for characterizing various quality problems. In this paper, we report an empirical study on 27,087 co-change commits of 6 open-source systems with the purpose of understanding the observed evolutionary coupling. We extracted fine-grained change information from version control system to investigate whether two files exhibit particular kinds of co-change relationships. We consider code changes on 5 types of program entities (i.e., field, method, control statement, non-control statement, and class) and identified 6 types of dominating co-change relationships. Our manual analysis showed that each of the 6 types can be explained by structural coupling, semantic coupling, or implicit dependencies. Temporal analysis further shows that files may exhibit different co-change relationships at different phases in the evolution history. Finally, we investigated co-changes among multiple files by combining co-change relationships between related file pairs and showed with live examples that rich information embedded in the fine-grained co-change relationships may help developers to change code at multiple locations. Moreover, we analyzed how these co-change relationship types can be used to facilitate change impact analysis and to pinpoint design problems.