  We study the spectral distortions of the cosmic microwave background
radiation induced by the Sunyaev-Zel'dovich (SZ) effect in clusters of galaxies
when the target electrons have a modified Maxwell-Boltzmann distribution with a
high-energy non-thermal tail. Bremsstrahlung radiation from this type of \\
electron distribution may explain the supra-thermal X-ray emission observed in
some clusters such as the Coma cluster and A2199 and serve as an alternative to
the classical but problematic inverse Compton scattering interpretation. We
show that the SZ effect can be used as a powerful tool to probe the electron
distribution in clusters of galaxies and discriminate among these different
interpretations of the X-ray excess. The existence of a non-thermal tail can
have important consequences for cluster based estimators of cosmological
parameters.
