The field of business process modeling has been beset by inter-model consistency problems which are mainly due to the existence of multiple variants of the same business process, for instance when models have been produced by different actors, or through the time by a same (or different) actor(s), as well as the possibility of its modeling from discrete and complementary perspectives (using different lenses).The aim of our research is manifold. First we aim to develop a framework (i) enabling situating new research activities as well as the existing approaches and (ii) targeting to master the inter-model consistency issue. Second, this framework shall offer the capability of handling business process models coherence issue (i) having in mind various modeling goals and targets/products and (ii) having in hand a wide range of problem statements and project situations requiring the use of a large catalogue of business process meta-models. Third, we have the ambition of determining gaps in current research with the aim of suggesting areas for further investigations in the area of inter-models consistency. In order to do so, this paper presents a systematic literature review (SLR) of consistency among business process models, where a total of 982 published papers extracted from the most relevant scientific sources, were considered, of which 41 papers, were ultimately included.