  We report the results of a search for X-ray emission from quasar host
clusters at moderate redshift using the {\sl ROSAT} HRI. We detect no emission
from the host clusters of 3C~263 (z=0.646) and PKS~2352-34 (z=0.706) to
3$\sigma$\ limits of 3.26 and 2.86 $\times$10$^{44}$\ ergs~s$^{-1}$
respectively (H$_o$=50, q$_o$=1/2) for clusters with r$_{core}$=125~kpc and
T=5~keV. These limits show that these quasar host clusters are not
substantially more X-ray luminous than optically or X-ray selected clusters of
similar richnesses at z$\gtrsim$0.5. We also report the possible detection of a
clump of X-ray emitting gas coincident with the brightest radio lobe of 3C~263.
This may be evidence for the existence of a clumpy ICM in the host cluster of
3C~263.
