Experiments on the effect of radio-frequency (RF) magnetic fields on the magnetic compass orientation of migratory birds are analyzed using the theory of magnetic resonance. The results of these experiments were earlier interpreted within the radical-pair model of magnetoreception. However, the consistent analysis shows that the amplitudes of the RF fields used are far too small to noticeably influence electron spins in organic radicals. Other possible agents that could mediate the birds' response to the RF fields are discussed, but apparently no known physical system can be responsible for this effect. Bioelectromagnetics 30:402–410, 2009. © 2009 Wiley-Liss, Inc.