A new method based on the use of the kinetic Vlasov equation is suggested to investigate oscillations and stability of inhomogeneous plasma in a helical magnetic field of cylindrical symmetry. A dielectric permeability tensor has been obtained for the plasma configuration mentioned. Exceeding the limits of hydrodynamics permits one to study oscillations with a wavelength of the order of the Larmor radius of the particles. In addition such an approach makes it possible to take into consideration interaction between the resonance particles and the wave thus permitting investigations of the "kinetic" mechanisms of oscillation buildup. These questions have also been discussed in an earlier article of one of the authors.The advance that is achieved in the present work consists of consideration of the curvature and shear of the magnetic field lines. With consideration of these quantities equations have been obtained that make it possible to investigate the behaviour of drift waves that are unstable in the case of a magnetic field with straight and parallel lines, and also waves that have been discussed by Suydam. We discuss the effect of a buildup of convective perturbations with resonance electrons that is connected with their motion along the lines of force. Such an effect takes place when the hdyrodynamic instability of Suydam is stabilized because of the large Larmor radius of the ions. The buildup effect mentioned is analogous to the "residual-instability" effect but considerably stronger than the latter if plasma pressure is small compared to magnetic pressure. This effect exists if there is a temperature gradient.It is shown that in a plasma that is in a gravitational field and confined by a straight magnetic field, an analogous effect of drift buildup of flute perturbations is possible