The Sacramento Peak Observatory flare records of 37 double-ribbon solar flares observed from 1968 to 1972 were examined for evidence of systematic motion of the brightness along the flare ribbons. Because of analogies between aurorae and solar flares and because of well-established motion along aurorae (e.g., the so-called westward traveling surge) one might expect such motions along the flare ribbon are common: we have, however, not been able to detect systematic motions in relation to the active region magnetic fields. The separation of the flare ribbons with time is well known and probably corresponds to the poleward motion of the aurorae during the auroral expansion phase. We found no counterpart in flares, however, of the equatorward motion of the aurorae during the auroral growth phase.