Recent innovative drives in hydraulics could introduce very competitive hybrid hydraulic vehicles (HHV), including also applications on personal vehicles or smaller trucks. Efficiency of these new drives is very good even in partial load conditions, and they have very good control characteristics (fast responses, and relatively low energy required for their control). These drives has been considered and analysed only in the serial HHV architecture. Traditional hydraulic drives have been regarded in the parallel HHV architecture mostly just for retrofitting or after-market applications for commercial heavy vehicles, while the hydraulic power-split architecture (generally without kinetic energy recuperation) has been applied just for slow and heavy vehicles (tractors, earth moving machines or special trucks). On the other hand, 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 or Renault IVT. 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 power-split hybrid hydraulic vehicle transmission which is based on their hybrid electrical counterpart. The mathematical model of the serial hybrid hydraulic transmission with the hydraulic transformer is developed from related bond-graphs, as well. Such models serve as a basis for the comparative analysis of the steady-state behaviour of the power-split HHV transmission and the serial HHV transmission. The analysis encloses the power train power flow. Related consideration of limitations and possible energy recuperation is given, too. Obtained kinematics mathematical models are the basis for their upgrade with dynamics using bond-graphs, which is necessary for more comprehensive analysis of hybrid hydraulic vehicles.