A theory for the oscillating two‐stream instability, in which the Ohmic heating of the electrons constitutes the nonlinearity, is developed for an inhomogeneous and magnetized plasma. Its possible role in explaining short‐scale, field‐aligned irregularities observed in ionospheric heating experiments is emphasized. The theory predicts that the initial growth of such irregularities is centered around the level of upper hybrid resonance. Furthermore, plane disturbances nearly parallel to the magnetic meridian plane have the largest growth rates. Expressions for threshold, growth rate, and transverse scale of maximum growth are obtained. Special attention is paid to the transport theory, since the physical picture depends heavily on the kind of electron collisions which dominate. This is due to the velocity dependence of collison frequencies, which gives rise to the thermal forces.