  We investigate the X-ray properties of the Parkes sample of flat-spectrum
radio sources using data from the ROSAT All-Sky Survey and archival pointed
PSPC observations. In total, 163 of the 323 sources are detected. For the
remaining 160 sources 2 sigma upper limits to the X-ray flux are derived. We
present power-law photon indices for 115 sources, which were either determined
with a hardness ratio technique or from direct fits to pointed PSPC data. For
quasars, the soft X-ray photon index is correlated with redshift and with radio
spectral index. Webster et al. (1995) discovered many sources with unusually
red optical continua among the quasars of this sample and interpreted this
result in terms of extinction by dust. Although the X-ray spectra in general do
not show excess absorption, we find that low-redshift optically red quasars
have significantly lower soft X-ray luminosities on average than objects with
blue optical continua. The difference disappears for higher redshifts, as is
expected for intrinsic absorption by cold gas associated with the dust.
Alternative explanations are briefly discussed. We conclude, however, that dust
does play an important role in some of the radio-loud quasars with red optical
continua.
