The definitive version is available at www.blackwell-synergy.com. Copyright Blackwell Publishing DOI : 10.1046/j.1365-8711.2000.03883.xUsing ROSAT observations, we estimate gas pressures in the X-ray-emitting medium surrounding 63 FRII radio galaxies and quasars. We compare these pressures with the internal pressures of the radio-emitting plasma estimated by assuming minimum energy or equipartition. In the majority of cases (including 12/13 sources with modelled, spatially resolved X-ray emission) radio sources appear to be underpressured with respect to the externalmedium, suggesting that simple minimum-energy arguments underestimate the sources’ internal energy density. We discuss possible departures from the minimum energy condition and ...