Zero‐frequency cyclotron waves, which can be excited by a variety of static perturbations, produce large‐scale disruption of relativistic electron beam equilibria. A study of their basic nonlinear properties and an examination of methods with which to achieve their effective suppression are presented. A simple set of envelope equations based on the signal‐particle equations of motion is derived. Both analytic and numerical solutions are obtained for the case of a uniform magnetic guide field. The envelope equations are then used to investigate methods of suppression. It is found that although a spatially steeply rising magnetic field is a key component in achieving such suppression, initial beam momentum flaring plays a crucial role. Relativistic, fully electromagnetic particle‐in‐cell simulations designed to examine methods of suppression are presented.