Conical distributions of oxygen ions are commonly observed at high altitudes above the auroral zone and in the cusp and cleft regions. The occurrence of these oxygen conics is well correlated with the intensity of waves in the ULF frequency range (of the order of a few hertz). It is shown that the inhomogeneity along the geomagnetic field lines allows a mode coupling between downgoing Alfv¿n waves (either proton cyclotron or magnetosonic) and upgoing oxygen cyclotron waves. Thus the electromagnetic energy flux carried downward with a large phase velocity can be transferred into a low phase velocity left-handed mode that resonates with oxygen ions and heats them. We estimate the corresponding rate of absorption of the incident. Alfv¿n waves as a function of the incidence angle and of the parameter &eegr;O+, which is essentially the product of the O+ relative concentration and the characteristic length of inhomogeneity of the magnetic field, normalized to the typical wavelength of the Alfv¿n waves, at the O+ gyrofrequency. For an incident magnetosonic wave (type II branch) the rate of absorption can be quite large (up to 20%), for &eegr;O+<10-2. This peak in the absorption coefficient, however, is obtained for a relatively narrow angular range, when the incidence angle is close to 90¿. An incident proton cyclotron wave (type III branch) is more likely to lead to efficient O+ heating because (1) two regimes, either at small or at large incidence angle, lead to an absorption rate up to 20%, (2) these maxima are only slightly dependent on the incidence angle, and (3) large absorption rates are expected over a relatively broad range of values of &eegr;O+(5¿10-3< &eegr;O+<10-1), compatible with those values that are expected throughout the magnetosphere. ¿ American Geophysical Union 1992