  We present the results of a search for X--ray luminous distant clusters of
galaxies. We found extended X--ray emission characteristic of a cluster towards
two of our candidate clusters of galaxies. They both have a luminosity in the
ROSAT bandpass of $\simeq10^{44}{\rm \,erg\,s^{-1}}$ and a redshift of $>0.5$;
thus making them two of the most distant X--ray clusters ever observed.
Furthermore, we show that both clusters are optically rich and have a known
radio source associated with them. We compare our result with other recent
searches for distant X--ray luminous clusters and present a lower limit of
$1.2\times10^{-7}\,{\rm Mpc^{-3}}$ for the number density of such high redshift
clusters. This limit is consistent with the expected abundance of such clusters
in a standard (b=2) Cold Dark Matter Universe. Finally, our clusters provide
important high redshift targets for further study into the origin and evolution
of massive clusters of galaxies. Accepted for publication in the 10th September
1994 issue of ApJ.
