This paper explores the properties of Rossby-type electrostatic electron plasma waves at frequencies very much less than the electron gyrofrequency but very much greater than the ion gyrofrequency. Such waves represent the electron counterpart of ion Rossby waves, which propagate at frequencies very much less than the ion gyrofrequency in a plasma in which the ambient magnetic field possesses a spatial gradient perpendicular to its line of action. This feature simulates the ‘β-effect’ that operates in the classical atmospheric Rossby wave: the wave dynamics associated with both ion and electron Rossby waves are structurally similar to those associated with wave perturbations in a rotating fluid, where the β-effect arises from a spatial gradient in the Coriolis acceleration. It is shown that this plasma β-effect gives rise to a ‘new’ mode of the Rossby type, and in addition considerably modifies the conical wave propagation properties characteristic of the electron cyclotron mode. The highly dispersive and anisotropic nature of these waves is described in terms of the topology of the wavenumber surfaces concomitant with plane-wave solutions of the wave equation for the system as a whole.