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A predictive automatic gear shift system is currently under development. The system optimizes the gear shift process, taking the conditions of the road ahead into account, such that the fuel consumption is minimized. An essential part of the system is a module that predicts the vehicle speed dynamics: This calculates a speed trajectory, i.e. the most probable vehicle speed the driver will desire for the upcoming section of the route. In the paper the theoretical background for predicting the vehicle speed, and simulation results of the predictive shift algorithm are presented.