In this paper a new approach to model a double clutch system is presented with the aim of obtaining a model suitable for real-time simulations. The proposed model is obtained with a proper coordinate transformation of the system equations: the transformed system is described by two new state variables that correspond to the weighted relative speeds of the clutch plates. In this way one unique model can be used to describe all the conditions of the clutch: free, slipping and lockup. Using this approach, very efficient numerical simulations can be performed without switching among different models and using variables which are not affected by chattering. Moreover this approach allows to implement a discrete model that can be used in real-time simulations for Hardware-in-the-loop automotive applications.