Hybrid Modelling is getting more and more important in technical and natural sciences. In these fields very complex systems and processes have to be simulated and therefore proper models must be developed. For complex systems different model structures for dynamical systems are available. One of the important model structures regarding complex dynamical systems are hybrid models. A hybrid model consists of several dynamical models and a state diagram where each state is described by a differential algebraic equation (DAE). This paper deals with benchmarks out of different fields of applications of this modelling approach. The first benchmark is an electrical circuit with linear devices and a diode as a nonlinear component. This example will show the influence of a simple model to the state space description or the corresponding differential algebraic description. The different models for the nonlinear behaviour of the diode influences the states of the state diagram. It is remarkable, that the different models for the diode results in a different hybrid model. The influence from these models on the diode can be observed. Another benchmark is the rotating pendulum. It is also described by a state diagram, in this special academic example a state diagram with two states. The two examples are representative, one out of the field of electrical engineering, one typical mechanical scenario. In the article two aspects will be considered. On the one side the modelling process of the electrical circuit will be observed in detail, especial the influence of different diode models on the structure of the states, and the state transition between the two states of the mechanical pendulum. On the other side also the need of a mathematical notation and description of the states and their transition will be discussed. In the end of the article some comments to the simulation of hybrid systems will be given.