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Recent innovative drives in hydraulics could introduce very competitive hybrid hydraulic vehicles (HHV). These drives has been considered and analyzed only in the serial HHV architecture. The series-parallel transmission architecture, also called power-split or e-CVT is highlighted as the most popular concept for full (strong) hybrid electric vehicles (HEV). The examples are one-mode power-split in Toyota Prius and two-mode (compound) power-split in GM-Allison EVT. Ambitions to make the hybrid hydraulic power trains better and more efficient would certainly require deeper analysis of more complex power-split (series-parallel) HHV transmission structures and related optimal controls. This paper presents bond graph based mathematical model of kinematics of a one-mode and a two-mode power-split hybrid hydraulic vehicle transmissions which are based on their hybrid electrical counterpart.