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Hydraulic turbines and pump-turbines are often required to operate in particular conditions at which they consume active power. To keep the power consumption at a minimum, it is necessary to dewater the runner to reduce the mechanical torque. One of these operating conditions is the synchronous condenser mode for the reactive power regulation of the grid. This operating mode requires the guide vanes closure and the lowering of the tail water below the runner by injecting pressurized air in the machine. Due to the air-water mixing, torque instabilities and air losses are observed in this operating mode causing the increase of the power consumption. In this thesis, the two-phase flow phenomena characterizing the operation in synchronous condenser mode are experimentally investigated; additionally, a theoretical framework is proposed to analytically describe and predict the observed flow phenomena and the corresponding power and air losses. These research challenges are addressed by means of four different contributions. First, the development of the sloshing motion of the air-water free-surface below the runner is qualitatively and quantitatively described by using high-speed visualization, pressure fluctuations measurements and automated image processing methods. Second, the development of an air-water ring in the vaneless gap between the runner and the guide vanes is studied by means of image processing and pressure fluctuations measurements to assess both the velocity and the pressure flow field. The pressure measurements in the vaneless gap make apparent a fluctuation due to the interaction of the rotating and stationary components and of the rotating two-phase flow. This interaction is revealed by the development of the Fourier series applied to the harmonic components of the system and the modal decomposition of the pressure signal. Third, the influence of the two-phase flow phenomena on the torque swings is investigated. Measurements of the resisting mechanical torque transmitted through the coupling of the runner and the shaft and corresponding to the absorbed mechanical power of the runner in the hydraulic turbine are performed; in addition, a study on the influencing operating parameters allows building an empirical predictive model of the torque. Finally, a study on the oxygen mass transfer in the water volume is performed by measuring the oxygen concentration in the spiral case and in the draft tube of the hydraulic turbine. A theoretical framework is developed on the equations governing the diffusion of oxygen in water and the diffusion coefficients are computed and validated with experimental results. Moreover, this study allows quantifying the air losses due to the diffusion of air in water and to model the diffusion process as a function of the operating parameters of the machine. The results allow the understanding of the two-phase flow mechanism in a turbine or pump-turbine operating in synchronous condenser mode causing instabilities and air losses. Furthermore, the predictive model of the power losses due to both torque and air consumption represents a novel achievement for the study of the two-phase flow in a turbine operating in condenser mode or, more in general, in dewatered condition, and for the control of the machine behavior and consumption on the full scale prototype.