The source of the anomalous resistivity that broadens shock fronts in a near‐collisionless plasma is attributed to the drift‐wave instability driven by the strong electron temperature gradients in the front. Whistler‐type waves propagating through the electrons in the plane of the shock front are treated by the fluid equations, with the ions kept unperturbed. The fastest growing unstable waves are found to propagate normal to the magnetic field, for which case the whistlers degenerate to convected waves. Resistivity is introduced such that it exactly cancels the growth rate due to the gradients, and the calculation is made self‐consistent by using this resistivity to deduce the magnitude of the gradient. The main results are simple formulas for the anomalous collision frequency and the resistive shock thickness&lgr;&eegr;. It is found that&lgr;&eegr; ≃ (Te2/mev1)1/2 (c/&ohgr;pe), where the subscripts 1 and 2 refer to conditions upstream and downstream of the shock, andvis the component of plasma velocity normal to the stationary shock. This result is found to be in reasonable agreement with the few available experimental results.