This paper investigates flute perturbations of a plasma that is in a helical, cylindrically symmetric magnetic field. In a geometricaloptics approximation an- equation has been obtained that relates the frequency and the wave vector of the flute perturbations of the plasma for an arbitrary relation of the gas pressure and the magnetic pressure and for an arbitrary ratio ϱ/λ of the Larmor radius of the ions to the wavelength. This equation, is used to obtain stability criteria and increments (decrements) of flute-type oscillations under conditions when the shear in the lines of force is insignificant. The stability condition obtained thus in an approximation of zero ion Larmor radius coincides with the corresponding results that follow from the hydrodynamics of Chew, Goldberger, Low. For small values of β and a finite ratio ϱ/λ a criterion was obtained for the stabilization of perturbations with finite ion Larmor radius.Consideration of interaction between resonance particles and the wave in a number of cases leads to the buildup of flute perturbations. It is shown that such a type of buildup—residual instability—in the case of a helical magnetic field differs essentially from the residual instability for a model with a force of gravity discussed in the paper by Rosenbluth. Krall and Rostoker which is due to differences in the direction of the drift of the resonance particles in the two cases.We have elucidated the connection between the waves that are responsible for flute instability of a hydrodynamic type and waves that have been revealed in the work of Yu. A. Tserkovnikov. We have considered transition to the case of a magnetic field with an infinitely large radius of curvature of lines of force. We have elucidated the question of the spatial structure (in a radial direction) of waves of the type discussed in Ref 5, and it has been shown that their radial wavelength is essentially connected with the ion Larmor radius, and the wavelength of hydrodynamic flute perturbations does not depend on the value of the latter.The effect of curvature of lines of force on flute perturbations of the type of transverse drift waves has been discussed. We have shown that for not too large a radius of curvature of the line of force R <a/β (a is the characteristic dimension for the change of plasma pressure), the instability predicted in the work of Krall and Rosenbluth [6] for such a type of oscillations in a field with R→ ∞ is stabilized.