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. Such models serve as a basis for the analysis of the steady-state behavior of two representative power-split HHV transmissions. The analysis encloses the power train power flow. Related consideration of limitations and possible energy recuperation is given, too. Obtained kinematics mathematical models provide the basis for their upgrade with dynamics effects using bond-graphs, and the example is given in the paper, as well.