The paper presents a numerical study of the effect of impurity gradients on collisionless drift waves. In the region where the usual simplifying hypotheses (wavelength transverse to the containment field greater than Larmor radii; longitudinal phase velocity differing greatly from thermal velocities) permitting analytical solution of the dispersion relation are not justified, this study provides a series of data on the extent of unstable zones and on the influence on the representative parameters of impurities. It confirms the appearance of an ion branch, possibly more unstable than the electron branch, which can develop on small wavelengths along the magnetic field and which cannot easily be stabilized by shearing the field lines. It is shown that the expected effect of this instability is to introduce into the contained plasma the impurities present at its boundary.