Previous calculations of the linear growth rate and two‐dimensional spatial structure of trapped‐electron modes are made more general and more accurate in several ways. First, an integral equation formulation of the eigenmode problem allows arbitrary values ofkr&rgr;i(wherekris the radial wavenumber and &rgr;iis the ion gyroradius) to be treated. Second, the ion response is generalized so that arbitrary ratios of the ion magnetic drift frequency to the mode frequency are allowed. Finally, the electron and ion collision operators have been improved to allow consideration of the plateau and Pfirsch–Schlu¨ter regimes in addition to the usual banana regime. It is therefore possible to follow the transition in toroidal geometry from the trapped‐electron mode to the collisionless and collisional drift modes. The method used involves expansion of the perturbed electrostatic potential in complete sets of radial and poloidal basis functions to convert the quasi‐neutrality integral equation into a matrix equation.