Solving analysis problems in physical worlds requires the representation of large amounts of knowledge. Recently, there has been much interest in using multiple models, in the engineering sense of the word, to capture the complex and diverse knowledge required during analysis. In this paper we represent physical domains as graphs of models, where the nodes of the graph are models and the edges are the assumptions that have to be changed in going from one model to the other. We introduce new, qualitative methods that automatically select and switch models during analysis. Our approach has been successfully used for three implementations in the fields of mechanics, thermodynamics, and fluid dynamics. © 1991.