As the development of turbocompounding and two-stage turbocharging technology, there are increasingly more two-stage turbine systems applied on vehicles. The two-stage turbine recovers waste heat from the exhaust and thus affects the engine performance significantly. However, the interaction pattern and mechanism between the two turbines have not been fully understood. The paper focuses on the characteristic of the two-stage turbine under steady and pulsating flows. Firstly, an analytical model for two-stage turbine is developed to investigate the relationships between the turbines load split and equivalent area ratio under steady condition. The pattern of the load split between the high pressure turbine (HPT) and low pressure turbine (LPT) is disclosed by the model and verified by experimental data. Second, the impact of pulse frequency and amplitude on the two-stage turbine unsteady characteristic is studied by 3D computational fluid dynamics. As frequency increases, the peak values of the HIT expansion ratio and rotor torque increase drastically while those of LPT change little. As the pulse amplitude increases, the cycle-averaged expansion ratio of HPT decreases while that of LPT increases. The cycle-averaged rotor efficiencies of HPT and LPT reduce 3.7% and 8.1% respectively under 1.6 A amplitude condition, when compared with steady condition. In order to understand the phenomenon, the reasons are also discussed in detail in the paper. (C) 2018 Elsevier Ltd. All rights reserved.