A theory is proposed to explain the selective heating of protons in a direction transverse to the geomagnetic field lines, which as been observed on board the AUREOL 3 satellite, as shown in a companion paper. This process, which occurs only in multicomponent plasma, ultimately leads to the formation of a conical distribution, inside and above the heating region. It is shown that magnetosonic Alfv¿n waves generated at higher altitudes can undergo a resonant mode conversion process as they propagate downward. The efficiency of the subsequent resonant absorption depends rather strongly on the propagation angle of the waves and on the relative abundance of H+ ions: up to 25% of the incident energy flux can be transferred to protons. The present theory moreover foresees that a strong parallel electric field component has to occur at the altitude at which the wave frequency matches the proton gyrofrequency. The corresponding spectra signature has been unambiguously identified in the AUREOL 3 data, together with an intensification of the upward flux of suprathermal protons, which indicates the presence of proton conics. We have verified that within the uncertainties of the measurements the energy balance between the incoming electromagnetic power and the outgoing flux of kinetic energy is well explained by the theory. ¿ American Geophysical Union 1993