We have analysed the X-ray emission from a sample of close Wolf–Rayet+O (WR+O) binaries using data from the public Chandra and XMM–Newton archives. Global spectral fits show that two-temperature plasma is needed to match the X-ray emission from these objects, because the hot component (kT > 2 keV) is an important ingredient of the spectral models. In close WR+O binaries, X-rays likely originate in colliding stellar wind (CSW) shocks, driven by the massive winds of the binary components. The CSW shocks in these objects are expected to be radiative because of the high density of the plasma in the interaction region. In contrast, our analysis shows that, in our sample of close WR+O binaries, the CSW shocks are adiabatic. This is possible only if the mass-loss rates of the stellar components in the binary are at least one order of magnitude smaller than the values currently accepted. The most likely explanation for the X-ray properties of close WR+O binaries is that their winds are two-component flows. The more massive component (dense clumps) has a role in the optical/ultraviolet emission from these objects, while the smooth rarefied component is a key factor in the X-ray emission from these objects.