Not yet reviewed by Pith; the record is open.

Relativistic shock models of gamma-ray bursts may be tested by comparison of their predicted low energy asymptotic spectral indices s to observations. Synchrotron radiation theory predicts that the instantaneous spectrum has s = - 1/3 and the spectrum integrated over the radiative decay of the electrons' energies has s = 1/2, with other cases lying between these limits. We examine the spectra of 11 bursts obtained by the Large Area Detectors on BATSE. One agrees with the predicted instantaneous spectrum, as does the initial portion of a second, and three are close to the predicted integrated spectrum. All the observed asymptotic spectral slopes lie in the predicted range. This evidence for relativistic shocks is independent of detailed models of bursts and of assumptions about their distances. Radiation observed with the predicted instantaneous spectrum has a comparatively smooth time dependence, consistent with the necessarily long radiation time, while that with the predicted integrated spectrum has a spiky time dependence, consistent with the necessarily short radiation time.