  We report on the first results from a redshift survey of a flux-limited
sample of X-ray clusters selected serendipitously from the ROSAT PSPC data
archive. We spectroscopically confirm 15 clusters in the range 0.3 < z < 0.7,
to a flux limit of ~ 3.9 x 10^-14 erg s^-1 cm^-2, over a survey area of 17.2
deg^2. The surface density of clusters in our survey is 2.0 (+0.4,-0.3) deg^-2,
in good agreement with the number density of cluster candidates detected using
algorithms designed to search for very extended sources. The number of clusters
detected between 0.3 < z < 0.7 is consistent with a prediction based on a
simple extrapolation of the local X-ray cluster luminosity function, which
indicates that over this redshift range no significant evolution in the cluster
population has taken place. These results are in conflict with recent claims
that the number density of X-ray clusters found in deep ROSAT PSPC pointings
evolves rapidly beyond z = 0.3.
