The design of lightweight robot arms introduces a degree of flexiblity in the individual links which renders the arm difficult to control. Solution of the control problem requires accurate and detailed mathematical models of the arm dynamics. A comprehensive survey of the current literature in this area has shown that although many such models exist, there is a great diversity in their structure, function, and applicability. The different objectives and techniques of model development which lead to this diversity are examined and summarized in this thesis. Bases for classification of the mathematical models and techniques of development are established, and a general development methodology is proposed for each class of model. Computer simulations of relevant portions of the model dewlopment are used to support these general development methodologies. The model development and classification processes are demonstrated by their application to several current models.