Most theories developed to explain interaction of impurities with a moving grain boundary involve a uniform excess impurity concentration distributed along a planar grain boundary. As boundary velocity increases, the excess impurities exert a net drag force on the boundary until a level is reached whereat the drag force no longer can balance the driving force and breakaway of the boundary from these impurities occurs. In this investigation, assumptions of a uniform lateral impurity profile and a planar grain boundary shape are relaxed by allowing both forward and lateral diffusion of impurities in the vicinity of a grain boundary. It is found that the two usual regions (drag of impurities by, and breakaway of a planar grain boundary) are separated by an extensive region wherein a uniform lateral impurity profile and a planar grain boundary shape are unstable. It is suspected that, in this unstable region, grain boundaries assume a spectrum of more complex morphologies and that elucidation of these morphologies can provide the first definitive description of the breakaway process and insight to more complex phenomena such as solid-solution strengthening, grain growth and secondary recrystallization.