Consideration is given to the resistive drift modes both at low frequencies and at ionic gyro-resonances of a non-uniform low-pressure plasma placed in an external magnetic field and in a longitudinal electric field. The spectra of instabilities are discussed for the kinetic.range of frequencies where the two-fluid hydrodynamical description is not applicable. Kinetic equations for ions and electrons with Landau collision integral are used. The conditions of instability are analysed on the ground of the local spectra obtained in the approximation of geometrical optics. Special consideration is given to the drift of the electrons. For every mode the criterion of stabilization by magnetic shear is specified. The paper comprises all resistive drift modes in the kinetic range of frequencies in a non-uniform plasma with current.