This work is devoted to the investigation of oscillations in the hydropower plants, consisting of synchronous generator, hydraulic turbine and speed governor. It is motivated by the accident happened on the Sayano-Shushenskaya hydropower plant in 2009 year. A mathematical model of the hydropower unit is based on the equations of Park-Gorev for synchronous generator described in detail in (Adkins, 1962), (Boldea, 2006), on the turbine equations taken from (Pervozvanskii, 1986), and on the simplified equation of governor suggested in (Merkur'ev and Shargin, 2008). For modeling the system parameters of the Sayano-Shushenskaya hydropower plant were used. Oscillations in zones, which were not recommended for operation, were found. The obtained results are consistent with full-scale tests results carried out for hydropower units of the Sayano-Shushenskaya hydropower plant in the late 80s of the XX century and published in (Gluhih, 1988).