Mathematical modeling and the simulation of complex physical systems are emerging as key technologies in engineering. The availability of static analyzers and automatic debuggers for detecting structural and numerical inconsistencies in the simulation models is crucial. To address this need, the authors propose a methodology for detecting and repairing overconstrained and underconstrained situations based on graph-theoretical approaches. Components and equations that cause the irregularities are automatically isolated, and meaningful error messages for the user are elaborated. The authors have implemented the AMOEBA (Automatic Modelica Equation-Based Analyzer) environment to support the development and specification of correct equation-based simulation models by applying graph-theoretical approaches and semiautomatic debugging techniques. The implementation architecture and preliminary experiments with a prototype debugger integrated in the symbolic and numeric engine, ModSimPack, of the Modelica language compiler are presented and discussed.