In the Tore Supra tokamak, magnetohydrodynamic instabilities can be destabilized by energetic particles produced by radio-frequency heating systems. This paper reports on experimental observations of two types of energetic particle driven internal modes: the electron fishbone and the beta-induced Alfvén eigenmodes (BAEs). The evolutions of these modes in frequency and radial position during core relaxation cycles were determined by their induced electronic temperature and density fluctuations. Electron fishbones were observed in the so-called oscillation regime, while BAEs' observations were performed in the sawtooth regime. The results show that the frequency and radial position of these two instabilities vary substantially during the core relaxation cycles. It indicates that an accurate description of these evolutions must consider the equilibrium profile alterations during the core oscillations.