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Continuously variable transmissions (CVTs) are usually used in small vehicles due to power limitations on the variable elements. Continuously variable power-split transmissions (CVPST) were developed in order to reduce the fraction of power passing through the variable elements [1,2]. The configuration presented in this paper includes a planetary gear train (PGT), which in combination with the CVT allows the power to be split and therefore increase the power envelope of the system. The PGT also provides a branch that can be used in a hybrid electric vehicle (HEV) operation through an electric motor. A conceptual design of a CVPST for a HEV is presented in this paper. The objectives are to show the different operational modes, with diagrams, perform a power analysis, develop the velocity and force equations and finally show the performance of the system with an example application.