The propagation of a one-dimensional combustion wave into a non-ionized gas at rest in the presence of an electromagnetic field is considered when ionization of the gas occurs across either the combustion wave or a preceding shock wave. The electric and magnetic fields in the undisturbed gas ahead of the waves are mutually perpendicular and orthogonal to the direction of wave propagation. It is shown that steady detonation occurs at a point which is analogous to the Chapman-Jouguet point of ordinary gasdynamic combustion theory. Numerical calculations are made of the state of the gas between and behind the waves in two particlar models, in both of which the upstream electric field is zero. The models are then equivalent to magnetogasdynamic phenomena in a perfectly conducting gas. First, the case of steady detonation is studied. Secondly, steady deflagration in a tube, closed at one end, is discussed.