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Transmission system power losses influence the efficiency of hybrid powertrains. Well-established parallel-hybrid-electric powertrains employ conventional transmissions that can be treated as single-input-single-output (SISO) systems. Novel parallel-hybrid-electric powertrains, which are not based on conventional transmissions, can increase the systems potential but increase the complexity as the transmission becomes a multiple-input-multiple-output (MIMO) system. For these MIMO-transmission systems, the losses can strongly depend on the selected transmission mode and on the input torques of the power sources. This paper presents a method to automatically model the power losses of such MIMO-transmission systems. This method consists of a mathematical analysis and a design analysis, and obtains the transmission power losses as a function of the selected transmission mode, the rotational speed of the wheels, and the torques of the power sources. The model includes gear meshing losses, gear churning losses, and bearing losses. Furthermore, an extended control strategy is proposed to ensure local optimality including the consideration of the multidimensional transmission power loss characteristics. A case study is presented to demonstrate the developed methods, and shows that the inclusion of the transmission losses in the powertrain model and control strategy can be considered relevant for the simulative assessment of novel parallel-hybrid-electric powertrains.