In the framework of the quasars-radio galaxies unification the radio-e
mitting lobes of FRII radio galaxies are pervaded by an intense quasar
radiation field. Inverse Compton (IC( scattering between the relativi
stic electrons and the IR-optical photons from a hidden quasar may pro
vide an important contribution to the X-ray emission of these radio ga
laxies. The soft X-ray emission properties of six strong, high redshif
t FRIIs (3C 277.2, 280, 294, 324, 356, 368) are compared with our mode
l expectations, taking into account also the contribution from the IC
scattering of the CMB photons with the radio electrons. Our estimates
are based on a typical quasar spectrum, derived from the infrared and
optical properties of a 3C quasar sample, and on the assumption of ene
rgy equipartition between relativistic particles and magnetic fields w
ith the same energy density in the electron and proton components and
with a fixed low energy cut-off in the particle distribution (Appendix
A). We find that the soft X-ray luminosities and spectra of five out
of six sources can be satisfactorily explained by our model with the e
xception of 3C 324 whose X-ray emission is probably dwarfed by that of
the galaxies' cluster of which this source is a member. In the case o
f 3C 277.2 our model requires a luminosity of the hidden quasar which
is in perfect agreement with that derived from spectropolarimetric stu
dies. In order to carry out the computations of the IC scattering of t
he hidden quasar photons, which an propagating radially outward, we ha
ve solved the anisotropic IC problem. The formal approach and relevant
formulae, which do not appear to be available in the literature, are
presented in the Appendix B. One important effect is the prediction th
at the observed X-ray emission associated with the two radio lobes wou
ld be asymmetric if the radio axis is inclined with respect to the pla
ne of the sky, the far-away lobe being the more luminous. The ratio be
tween the X-ray luminosities of the two lobes is derived for several v
alues of the inclination of the radio axis. However, the predicted ang
ular sizes of these distant radio galaxies are small and difficult to
be resolved with present X-ray facilities.