The reported continuum spectra (~20 keV-2 MeV) of most γ-ray bursts resemble a simple exponential1-4. Hence, the conventional view is that they are the optically thin free-free (bremstralung) emission of a hot thermal plasma (kT >~ 100 keV with the exception of a few soft events, notably the 5 March 1979 event). I show here that: (1) independent of the source distance, there is an inherent difficulty with the free-free interpretation if the sources are indeed neutron stars with magnetic field B ≳ 1012 G, because the synchrotron emissivity of these hot thermal electrons would greatly exceed then free-free emissivity for any reasonable electron density consistent with τes << 1 required by observations; (2) the spectral data can be fitted equally well, if not better, by optically thin thermal synchrotron spectra of mildly relativistic (kT ~ mc2) electrons; (3) the absence of observable low-energy turnover due to synchrotron self-absorption (or high energy Compton distortion) puts interesting upper limits to the source of luminosity and distance. Most sources are noncosmological (<10 kpc-1 Mpc) but not necessarily as nearby as some authors have suggested using the free-free spectral interpretation (see, for example, ref. 2).