Doppler shifts of emissions from neutral species have been observed for the first time in a positive column of a de glow discharge. For a detailed study, we have chosen emissions of H-2 and its isotopomers in a hydrogen discharge using a high resolution Fourier-transform spectrometer. Experimetal evidence supports the conclusion that the observed shifts derive from momentum transfer during electron-molecule collisions that produce the emissive excited states. A theoretical model has been formulated to relate Doppler shifts to the drift velocity of electrons in the discharge as well as to the momentum transfer of electron-molecule collisions. Predictions based on the model are consistent with the experimental observations.