Instability of the drift-dissipative type, of a weakly ionized non-isothermal plasma in crossed electric and magnetic fields (Simon; Hoh) has been studied in the quasi-classical approximation for two cases: (a) Ωeτe ≫ 1, Ωiτi ≫ 1, (b) Ωeτe ≫ 1, Ωiτi ≪ 1. The increment and frequency of the instability of such a plasma against potential disturbances have been deduced in the linear approximation. Equations of strong turbulence evolved with the aid of Mikhailovskii's diagram method have been used in estimating the maximum value of the spectrum function of the electric field of oscillations and of the coefficient of turbulent diffusion. The concluding part of the paper presents a set of equations of strong turbulence in the dimensionless form suitable for computer analyses.