Ion orbits and equilibrium ion flow in crossed electric and magnetic fields are examined for the case of a strongly nonuniform electric field such as found in edge plasmas of tokamak fusion experiments and in space plasmas. It is shown that theE×Bdrift approximation no longer applies, either to the motion of a single ion or to the collective response of the ion species when the absolute value of the shear parameter, ‖&zgr;‖, defined as the absolute value of the ratio of the gradient ofE×Bspeed to ion gyrofrequency, is order one. It is also found that the ion velocity is strongly dependent on the electric field geometry. The results suggest that the existence of a strongly sheared electric field does not necessarily indicate the existence of strongly sheared plasma flow, and that the spatial shape of the electric field, when ‖&zgr;‖ is order one, may be a dominant factor in determining the resulting plasma flow speed.