A hydraulic generating system (HGS) may undergo Hopf bifurcations or limit point bifurcations before the occurrence of low-frequency oscillations (LFO). These oscillations severely limit the power trans-mission capacity and even threaten the stability of the power grid in some situations. Hence it is increasingly crucial to have a clear understanding of LFO in bifurcation scenarios. This problem becomes even more complicated with parametric uncertainties in power systems as it is always challenging to efficiently handle LFO under such conditions. To address this challenge, a mathematical model of a HGS is established which is then utilized to evaluate the sensitivity of state variables against parametric uncertainties. Subsequently, two bifurcation scenarios with variations in two sensitivity parameters (the proportional and integral adjustment coefficients) are analyzed to demonstrate the interactions between oscillation modes and bifurcations. Finally, the results are presented in terms of oscillation indicators of bifurcation scenarios. These indicators include the eigenvalue, frequency, damping and participation factor. One of the most important results shows that the governor provides positive damping to HGS and introduces ultra-low frequency oscillations to the system under certain conditions. The proposed approach and analytical results provide a useful tool for analyzing LFO in a HGS for bifurcation scenarios. (c) 2020 Elsevier Ltd. All rights reserved.