The propagation of a plane electromagnetic wave in a magnetoelectric (ME) medium is discussed with respect to the case where the (ME) suceptibility α can be expressed as a nondiagonal tensor. Concerning the propagation in the x direction, we obtain the theoretical result that the phase velocity changes with a reversal of propagating direction. We also examine the behavior of a plane wave which is normally incident on a perfectly conducting wall. The standing wave in this case shows the interesting behavior that the back-ward or progressive wave is due to the existence of ωα Further-more, the Fresnel's equations are analyzed with respect to the ME suceptibility constant, and these results show that, when the magnitude of the ME suceptibility exceeds a cirtain value, there exists only progressive or reflected wave in one direction and no wave in the other.