We present a theoretical analysis of the effect of multiple impurity scattering on the various equilibration processes between the edge states in the integer quantum Hall effect. In the Born (single-scattering) approximation, which is valid for very low impurity concentrations, it was found that both the elastic and inelastic (phonon) scattering between the edge states are suppressed in high magnetic fields. In the presence of higher impurity concentrations, the higher-order terms in the perturbation series dominate the equilibration process. We use arguments similar to those in the variable-range-hopping theory to derive a multiple-scattering-assisted equilibration rate between neighboring edge states. The results show an exponential suppression of scattering, as compared with the Gaussian suppression in the Born approximation. We also found that the momentum-energy-conservation requirements for phonon emission are relaxed in this mechanism. © 1991 The American Physical Society.