  The negative evolution found in X--ray clusters of galaxies limits the amount
of available hot gas for the inverse Compton scattering of the Cosmic Microwave
Background (the Sunyaev--Zel'dovich effect). Using a parametrisation of the
X-ray luminosity function and its evolution in terms of a coalescence model (as
presented in the analysis of a flux limited X-ray cluster sample by Edge et al.
1990), as well as a simple virialised structure for the clusters (which
requires a gas to total mass fraction $\approxgt 0.1$ in order to reproduce
observed properties of nearby clusters) we show that the Compton distortion $y$
parameter is about two orders of magnitude below the current FIRAS upper
limits. Concerning the anisotropies imprinted on arcmin scales they are
dominated by the hottest undetected objects. We show that they are negligible
(${\Delta T\over T}\approxlt 10^{-7}$) at wavelengths $\lambda\approxgt 1$~mm.
At shorter wavelengths they become more important (${\Delta T\over T}\sim
10^{-6}$ at $\lambda\sim 0.3$~mm), but in fact most clusters will produce an
isolated and detectable feature in sky maps. After removal of these signals,
the fluctuations imprinted by the remaining clusters on the residual radiation
are still much smaller. The conclusion is that X-ray clusters can be ignored as
sources of Cosmic Microwave Background fluctuations.
