Abstract In fullerene anions C60n−, the n electrons outside closed shells occupy t1u triplet electronic states. Jahn–Teller (JT) coupling between these states and 5-fold h-type vibrations has important consequences for many properties of the fullerene anions. It is therefore important to understand the JT effect experienced by these ions from a theoretical point of view. We will study the cases of n=2 and 4, where the lowest adiabatic potential energy surface is found to consist of a two-dimensional trough in linear coupling. The motion of the system therefore consists of vibrations in three directions ‘across’ the trough and pseudo-rotations in two directions around the trough. Analytical expressions for states of the system that reflect this motion are obtained and the resultant energies determined.