The hybridization of automotive powertrains increases due to legislative regulations in order to reduce emissions. Hybrid Dual-Clutch Transmissions, where an electric machine is included in the transmission, play a key role in this topic because of their significantly lower losses in contrast to other transmission concepts. On the one hand the hybridization results in new functionalities such as boosting, electric drive and many more. But on the other hand it also increases complexity and the necessity of improved control algorithms because of the advanced interaction of the engine, the electric machine, the clutches and the vehicle. For a good drivability a fast and precise control of all actuators is mandatory. The key elements here are the clutches as they connect or decouple the propulsion sources from the wheels. In order to meet these requirements, two model-based control approaches are elaborated in this contribution. Beginning with a detailed nonlinear parametric model, it is reduced with two different approaches and the singular perturbation theory. With the reduced models a position-based and a pressure-based controller are designed, both with a Two-Degree-of-Freedom structure that contains a flatness-based feedforward component, a linear–quadratic regulator with integrator as feedback component, an observer for the stiff system, and a trajectory generation module. Both controllers show a fast control response and only small tracking errors in experiments performed on a transmission test bench, where the filling of the clutch and the tracking of several specific torque profiles, such as a fast engagement process are validated.