The propagation of lower‐hybrid waves in the presence of ponderomotive density fluctuations is considered. The problem is treated in two dimensions, and in order to be able to correctly impose the boundary conditions, the waves are allowed to evolve in time. The fields are described byiv&tgr;−F v&xgr; d&zgr;+v&zgr;&zgr;+‖v‖2v=@qL0, wherevis proportional to the electric field, &tgr; to time, and &zgr; and &xgr; measure distances across and along the lower‐hybrid ray. The behavior of the waves is investigated numerically. If the amplitude of the waves is large enough, the spectrum of the waves broadens and their parallel wavelength becomes shorter. The assumptions made in the formulation preclude the application of these results to the lower‐hybrid heating experiment on Alcator‐A. Nevertheless, there are indications that the physics embodied in this problem are responsible for some of the results of that experiment.