Security, risk and compliance are increasingly important issues in enterprise modelling. An analysis of real world scenarios for banking has shown that today's "best practices'' based on informal techniques are insufficient and should be replaced by adequate formal approaches. For this purpose, visual enterprise models based on algebraic graph and model transformation are proposed in this thesis, where the following two typical problem areas are considered: (1) Behaviour Analysis and Optimization of Visual Enterprise Process Models (2) Conformance Analysis of Enterprise Process and Service Models The first problem is solved by new concepts and results concerning behaviour analysis of visual languages, especially analysis of permutation equivalence of graph transformations based on Petri nets. In order to tackle the second problem area, model transformations based on triple graph grammars are introduced with new results concerning analysis and optimization enabling automated support for sound integration and conformance checks between different models. The new results in the area of graph and model transformation are developed in the general framework of M-adhesive transformation systems. They can be instantiated to a large variety of high-level replacement systems and applied not only to enterprise modelling, but also to several other application domains. Last but not least, the new tool AGT-M provides automated tool support for simulation, analysis and optimization in various case studies.