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The main aim of this paper is to investigate the performance of hybrid electrical vehicles (HEVs) using single and dual epicyclic power split transmissions (PST). The development of PST has been a crucial feature in the technological success of hybrid driveline vehicles. In this paper, single and twin epicyclic power split transmissions models are analyzed and the relationships of speed and torque of the engine, motor and generator are developed. The models are further extended to include all subsystems and a controller designer to be fitted in a typical hybrid electrical vehicle (HEV). Computer programmes for the analysis of epicyclic transmission based on a matrix method are developed and used. In addition, the performance and control strategy of the new system is presented. Three vehicle models are built-up; namely: traditional ICE vehicle, HEV with single epicyclic gearbox, and HEV with twin epicyclic gearbox. The vehicles are simulated over typical driving cycles.