CLUSTERS of galaxies are the largest gravitationally bound systems in the Universe and therefore provide important constraints on the formation and evolution of large-scale structure. Cluster evolution can be inferred from observations of the X-ray emission of the gas in distant clusters, but interpreting these data is not straight-forward. Tn a simplified view, clusters grow from perturbations in the matter distribution, and the intracluster gas is compressed and shock-heated by the gravitational collapse(1). If the gas is in hydrostatic equilibrium the resulting X-ray emission is related in a simple way to the evolving gravitational potential. But if processes such as radiative cooling or pre-collapse heating of the gas are also important, the X-ray evolution will be strongly influenced by the thermal history of the gas. Here we present the results of a faint flux-limited sample of X-ray selected clusters observed by Rosat. Very few distant dusters have been identified, and their redshift distribution seems to be inconsistent with simple models based on the evolution of the gravitational potential, Our results thus suggest that radiative cooling or non-gravitational heating of intracluster gas must be important in the evolution of clusters.