Differential energy spectra of electrons observed in an auroral breakup show evidence that an incident electron beam of energy E=6--13 keV, width of 2--5 keV, and variable intensity was stabilized over a period of at least several minutes by the oscillating two-stream instability in the manner previously described by Papadopoulos and Coffey. The critical observed feature predicted by these authors' calculation is a tail with differential flux dj/dE∝E0.5. This tail is much too intense to be attributed to the effects of collisions with atmospheric constituents. It is possible that the tail is part of the beam itself, i.e., produced higher up, but there are at least two arguments against this: first, the observations indicate that the tail approaches isotropy, whereas the beam is mostly downcoming, and second, the tail is observed as low as 130 km; the portion of the tail below 1.5 keV would have been absorbed by the atmosphere at greater heights if it had been incident from above. The observations support the hypothesis that the tail electrons are produced locally and by the proposed stabilization process. Implications are briefly discussed.