It is known that if single frequency continuously transmitted ultrasound or electromagnetic energy is reflected from ‘‘straight line flow,’’ defined here as one or more scatterers moving with constant velocity along an infinite straight line, the Doppler effect will shift the echo spectrum center frequency from the transmitted value, and broaden its bandwidth. It is proved thatifsuchstraightlineflowisshiftedlaterallyorinrangeanywhereinthefield,i.e.withoutchangeoforientation,itsDopplerbandwidthremainsunchanged. (The ‘‘Doppler bandwidth’’ is here defined as the frequency difference between the extrema of the echo power spectrum.) The theorem holds true even though the time domain echo changes dramatically with motion of the flow path, and is believed to be valid for electromagnetic as well as ultrasound waves. Its implications with respect to flow measurement, as well as preliminary experimental and computational confirmation, will be discussed.