In a series of two papers, we investigate the setting up and solving of conditional models within an equation-based modeling environment. Conditional models arise in chemical engineering when modeling systems involve physicochemical discontinuities, such as phase transitions. Grossmann and Turkay (Grossmann, I. E.; Turkay, M. Comput. Chem. Eng. 1996, 20, S339-S344) show how one can represent conditional models as algebraic systems of disjunctive equations. In this paper we identify the modeling capabilities needed for the efficient representation and solution of conditional models. We then describe modeling tools for the performance of each of the identified tasks: conditional configuration of a model structure, conditional compilation, and conditional execution of procedural statements. We next describe the details of the computer implementation of these tools and show how the expressiveness of an equation-based modeling language increases with their incorporation. Finally, we present several chemical engineering examples to demonstrate the scope of application of the proposed extensions. In Part 2 we investigate two approaches, a new complementarity formulation and the boundary crossing algorithm of Zaher (Zaher, J. J. PbD. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1995), for solving a special subclass of conditional models exhibiting continuity across boundaries.