Using ROSAT observations, we estimate gas pressures in the X-ray-emitting m
edium surrounding 63 FRII radio galaxies and quasars. We compare these pres
sures with the internal pressures of the radio-emitting plasma estimated by
assuming minimum energy or equipartition. In the majority of cases (includ
ing 12/13 sources with modelled, spatially resolved X-ray emission) radio s
ources appear to be underpressured with respect to the external medium, sug
gesting that simple minimum-energy arguments underestimate the internal ene
rgy density of the sources. We discuss possible departures from the minimum
-energy condition and the consequences of our result for models of the dyna
mics of radio galaxies, in particular self-similar models.