The effect of a large-amplitude, spatially uniform electric field at lower hybrid frequency, which is applied across the static magnetic field, on the dispersion relations for low-frequency drift waves (ω ≪ ωci) and drift cyclotron waves (ω ≃ ωci) in a collisionless plasma is investigated. It is found that the lower hybrid field can parametrically excite or suppress the drift waves. Expressions are derived for the threshold electric field required for such effects. A particularly interesting result is the possibility of exciting some new macroscopic instabilities when wave-particle resonances are ignored. The results of this investigation are likely to be relevant to some of the recently proposed schemes using lower hybrid waves for heating plasma ions up to fusion temperatures.