A range of influences, both technical and organizational, has encouraged the widespread adoption of Enterprise Systems (ES). The integrated and process-oriented nature of Enterprise Systems has led organizations to use process modelling as a means of managing the complexity of these systems, and to aid in achieving business goals. Past research illustrates how process modelling is applied across different Enterprise Systems lifecycle phases. However, no empirical evidence exists to evaluate what factors are essential for a successful process modelling initiative, in general or in an ES context. This research-in-progress paper reports on an empirical investigation of the factors that influence process modelling success. It presents an a-priori process modelling critical-success-factors-model, describes its derivation, and concludes with an outlook to the next stages of the research.