e-Health Networks require cost-effective approaches for routine operation to achieve long-lasting sustainability. By using a model to represent (i) the network's enterprise functions, (ii) the applications used and (iii) the physical implementations, the tasks of management, adapting to changes and providing continued maintenance can be effectively supported. The paper discusses approaches for modeling, assesses their usefulness for the above tasks and decides on the use of the 3LGM meta model. Based on this concept, three ways for modeling the specific properties of an e-Health network are presented, leading to the decision to represent the hospitals involved in only one layer. As a result the model derived is presented, assessed and proved to support strategic management, day-to-day maintenance and documentation.