During their collisionless motion in the shock front electrons are efficiently accelerated by the de Hoffman-Teller cross shock potential. Inside the shock ramp two electron beams are formed: those which are accelerated from upstream to downstream and those which come from the downstream region to match the upstream distribution. This electron distribution is two-stream unstable. We estimate the typical temporal and spatial scales on which the instability develops. We argue that this instability could result in fast relaxation of the electron beams and formation of the observed flattopped distributions. ¿ 1999 American Geophysical Union