The effect of an r.f. electric field of frequency Ω, oriented parallel to a static magnetic field, having a gradient in the radial direction of the plasma column, on the drift dissipative instability is studied using a two-fluid macroscopic approach. This method is identical to that developed by two of the authors in their 1969 paper on the stabilization of drift oscillations by a uniform r.f. field. When Ω is greater than the collision frequency of the electrons, the presence of a gradient of the r. f. field reduces the minimum value of this field required for complete stabilization by more than an order of magnitude.