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Object-oriented modeling with declarative equation based languages often unconsciously leads to structural inconsistencies. Component-based debugging is a new structural analysis approach that addresses this problem by analyzing the structure of each component in a model to separately locate faulty components. The analysis procedure is performed recursively based on the depth-first rule. It first generates fictitious equations for a component to establish a debugging environment, and then detects structural defects by using graph theoretical approaches to analyzing the structure of the system of equations resulting from the component. The proposed method can automatically locate components that cause the structural inconsistencies, and show the user detailed error messages. This information can be a great help in finding and localizing structural inconsistencies, and in some cases pinpoints them immediately.