On the basis of Boltzmann's kinetic equations hydrodynamic equations have been obtained for the ions and electrons of a fully ionized collisional plasma in a strong inhomogeneous magnetic field under assumptions characteristic of works on "drift" instability. These equations are a generalization of the results of Mikhailovsky's work on an inhomogeneous magnetic field and make it possible to solve problems connected with the hydrodynamic drift instability of plasma in the presence of shear, curvature of the lines of force and inhomogeneity of the absolute value of the magnetic field.