The method of multiple scales is used to derive a nonlinear Schrödinger equation, which describes the nonlinear evolution of electron plasma ‘slow waves’ propagating along a hot cylindrical plasma column, surrounded by a dielectric medium and immersed in an essentially infinite axial magnetic field. The temperature is included as well as mobile ion effects for all possible modes of propagation along the magnetic field. From this equation the condition for modulational instability for a uniform plasma wave train is determined. © 1987, Cambridge University Press. All rights reserved.