AbstractHere we suggest that efficient stochastic particle re–acceleration in galaxy clusters may be driven by compressible modes. The damping of these modes is severely dominated by the TTD–resonance with thermal electrons and protons in the ICM. However, a small energy flux of these modes may be channelled into particle re-acceleration and this gives re-acceleration times of the order of ∼ 10⁸ yrs, sufficient to mantain GeV radiating electrons in the ICM.