The possibility that plasma oscillation bursts (“fish-bones”) could be excited in a fusion burning plasma is pointed out. The relevant instability is brought about by the resonant interaction between an m0 = 1 mode and slowed down alpha particles in the 300- to 400-keV energy range. The resulting resonant scattering of these intermediate energy particles does not appear to affect significantly the alpha-particle heating power. The drift of the banana orbits of 3.5-MeV alpha particles in the fluctuating field associated with this instability and the possible secondary instabilities driven by the locally depleted alpha-particle distribution function may have more serious consequences.