We present the results of a search for X-ray luminous distant clusters
of galaxies. We found extended X-ray emission characteristic of a clu
ster toward two of our candidate clusters of galaxies. They both have
a luminosity in the ROSAT bandpass of similar or equal to 10(44) ergs
s(-1) and a redshift greater than 0.5; thus making them two of the mos
t 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 distan
t X-ray luminous clusters and present a lower limit of 1.2 x 10(-7) Mp
c(-3) for the number density of such high-redshift clusters. This limi
t is consistent with the expected abundance of such clusters in a stan
dard (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.