Due to the strong growth of electromobility, the demand for compact and efficient electric motors is increasing. Currently, mainly permanent magnet synchronous machines are used for electric vehicles. The use of rare earth materials in the magnets is cost-sensitive and decreases the efficiency in the field-weakening range at high speeds. An alternative is the use of electrically excited synchronousmachines. Electrically excited synchronous machines are often used as generators. For this purpose, power density, wear and operation over the entire operating range are not relevant but are essential for use in electric vehicles. This doctoral thesis presents an inductive electrically excited synchronous machine with a contactless energy transmission system. The transmission system is integrated inside the rotor shaft to reduce axial length. The model of an electrically excited synchronous machine is extended by considering saturation. An analytical calculation for the transformation ratio is derived. Furthermore, rotor shape is investigated for operation in field weakening. During the design process, thermal and mechanical requirements are considered in addition to an electromagnetic design, and the topology selection of the contactless energy transmission system is explained. An electromagnetic optimization method is developed and applied to minimize torque ripple and optimize efficiency in the drive cycle. For this purpose, a vehicle model is used to derive a relevant operating range from the driving cycle. In simulation, the machine losses in the driving cycle are reduced by 40%compared to referenced permanent magnet excited synchronous machine.