Modern pump-turbines are subject to frequent switching between the pumping and generating modes with extended operation under off-design conditions. Depending on the specific speed of the pump-turbine, the discharge-speed as well as torque-speed generating mode characteristics at constant guide vanes opening can be "S-Shaped". In such a situation, the machine operation may become strongly unstable at runaway speed and beyond, with a significant increase of structural vibrations. Moreover, seeing that a stable runaway operating point is difficult to be reached, the synchronization with the electrical network in safety conditions becomes impossible. This thesis explores the hydrodynamics of a low specific speed Francis type reversible pump-turbine reduced scale model, while operating at off-design conditions in generating mode and experiencing unstable operation at runaway due to the presence of a positive slope on the characteristic. More precisely, this work focuses particularly on normal operating range, runway and very low positive discharge operating conditions at 10° guide vanes opening angle. The methods employed in this process are the experimental and the numerical simulation ones. The experiments performed in this research involve: high-speed flow visualizations using tuft or injected air bubbles, PIV measurements in the stator, and wall pressure measurements in both stationary and rotating frames. When starting from the normal operating range and augmenting the impeller speed, a significant increase in pressure fluctuations, mainly in the guide vanes region, is noticed. Spectral analysis of pressure measurements in the stator shows a rise of a low frequency component (∼70% of the impeller rotational frequency) at runaway, which further increases as the zero discharge condition is approached. Analysis of the instantaneous pressure peripheral distribution in the vaneless gap reveals one stall cell rotating with the impeller at sub-synchronous speed. The same low frequency component is identified in the rotating frame pressure measurements as well. In the rotating frame referential, the stall cell covering about half of the impeller circumference revolves with about 30% of the impeller rotational speed in counterclockwise direction. High-speed flow visualizations, using injected air bubbles and tuft, reveal a quite uniform flow pattern in the guide vanes channels at the normal operating range. In contrast, when operating at runaway, the flow is highly disturbed by the rotating stall passage. The situation is even more critical at very low positive discharge, where backflow and vortices develop in the guide vanes channels during the stall passage. In addition, the wires position in the guide vanes and at the impeller outlet suggests a flow state similar to the one in reverse pump mode operation. PIV measurements in the guide vanes region confirm the outflow at the impeller inlet. Moreover, it is found that the pumping phenomenon in the guide vanes channels is performed with the help of a vortex. Indeed, this is the way the flow may change the direction by 180° from the vaneless gap to the upstream side of guide vanes. Therefore, at the low positive discharge condition, the flow alternates between turbine and reverse pump modes during one rotating stall revolution. Unsteady incompressible turbulent flow numerical simulations are performed in the full reduced scale model water passage domain by using the Ansys CFX code for few operating points. The finite volume method is used in order to solve the incompressible unsteady Reynolds-Averaged Navier-Stokes equations. The hybrid RANS-LES turbulence model, based on the von Karman length scale for blending function, which is called SAS-SST, is employed in simulation. The pressure fluctuations, produced by the rotor-stator interaction, are in good agreement with the experiments for both normal operating range and off-design conditions. By contrast, the rotating stall is captured at runaway. As for the expected organized rotating stall, it is not well defined at low discharge operating condition, even if several impeller channels are found to pump. Despite the fact that numerical simulation results are not quantitatively accurate, their qualitative analysis is used to draw the flow pattern inside the impeller in the presence of rotating stall. Thereby, it is shown that two stationary counter-rotating large vortices dominate the impeller channels flow. Their source is the large flow separation at the impeller inlet. This flow configuration can provide both a positive and a negative discharge, with a smooth transition between the turbine and reverse pump modes. In addition, a third vortex is generated at the impeller outlet during the reverse pump mode as a result of the relative velocity direction. To sum up, the flow in a pump-turbine operating at off-design conditions in generating mode, in the so-called "S-shaped" region of characteristics, is dominated by one stall cell rotating with the impeller at sub-synchronous speed in the vaneless gap between the impeller and the guide vanes. It is the result of flow separation developed at the inlet of the impeller channels that leads to their blockage. Moreover, at low positive discharge condition, the stalled impeller channels are found to pump, leading to backflow and vortices development in the guide vanes region. The rotating instability generates hydraulic unbalance and strong structural vibrations.