Low Frequency Perturbations in Inhomogeneous Plasmas The waves and instabilities produced by inhomogeneous currents J 0z (x) in plasmas along the initially constant magnetic field are investigated. The total zero- B order magnetic field is twisted and becomes space dependent . In heavier ion (like barium) plasmas the ion dynamics can be ignored in the presence of sheared flow of electrons. Electrostatic current-driven wave with the frequency near / (where | ln / | , / and is the perpendicular wavenumber) can exist in such plasmas and it becomes unstable under certain conditions. The nonlinear equations for this mode have been derived and stationary solutions in the form of vortices and solitons have been obtained. Due to sheared flow of electrons and ions in the presence of stationary dust, a low frequency electrostatic current-driven drift like wave with real frequency / has also been proposed to exist in dusty plasmas. The nonlinear equations for this wave including the effects of density gradient have been derived. The effects of kappa distribution of electrons have also been investigated. D''Angelo''s mode is modified in the presence of superthermal electrons. In the nonlinear regime the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn''s magnetosphere corresponding to negatively charged dust grains. The very low frequency wave at dust time scale can also be produced by the sheared currents if dust is assumed to be dynamic. These very low frequency waves and instabilities with small growth rates can be important in the planetary and cometary magnetospheres due to the interaction of solar wind. In the nonlinear regime these waves give rise to electrostatic structures such as vortices and solitons. A comparison of these very low frequency current-driven dust waves with the current-driven ion waves is also presented to point out analogous physical pictures with different temporal and spatial scales. The theoretical model is a general one and here it is applied to Saturn''s magnetosphere for illustration. ix The global drift mode is also studied in a plasma bounded in a cylinder having Gaussian density profile. The effect of magnetic shear on the wave propagation along density gradient is studied in a Cartesian geometry assuming absorbing boundary. It is found that the wave amplitude is reduced when two-ion species are present (with the same concentration) compared to pure electron-ion plasma.