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Expert problem-solving strategies in many domains require the use of detailed mathematical techniques coupled with experiential knowledge about how and when to use the appropriate techniques. In many of these domains, such techniques are made available to experts in large software packages. In attempting to build expert systems for these domains, we wish to make use of these packages, and are therefore faced with an important problem: how to integrate the existing software, and knowledge about its use, into a practical expert system. The expert knowledge is used, in dynamic selection and interpretation of appropriate programs and parameters, to reach a successful goal in the problem solving. We describe the framework of a hybrid expert system for representing problem-solving knowledge in these domains. This hybrid system may be characterized as consisting of a production system and mathematical methods. The software package is reorganized as necessary to map it into the mathematical-method representation of a hybrid system. This approach has evolved out of an effort to build an expert system for performing well-log analysis, ELAS (expert log analysis system).