The effect of model simplification assumptions on the differential index of differential-algebraic equation (DAE) process models is investigated in this paper. A process model is considered as the set of model equations in the form of a DAE system together with a suitable specification forming a zero degree of freedom model. Such a model is described by its equation variable graph. The effect of model simplification assumptions is analyzed by describing them as graph transformations acting on the structure graph of the process model. Efficient incremental graph-theoretic algorithms are proposed to follow the changes in the variable-equation assignments and for analyzing the changes in the differential index during the model simplification phase of the modelling process. The algorithms provide guidelines on how to modify the specification in order to obtain an index I model after model simplification. A case study with different transformations is used to demonstrate the operation of the algorithms and to follow the effect of constant and steady-state assumptions on the differential index of a simple process model. (C) 2003 Elsevier Ltd. All rights reserved.