  In almost any scenario for 'cosmological' gamma-ray bursts (and in many
models where they originate in our own Galaxy), the initial energy density is
so large that the resulting relativistic plasma expands with $v\sim c$
producing a blast wave ahead of it and a reverse shock moving into the ejecta,
as it ploughs into the external medium. We evaluate the radiation expected from
these shocks,for both cosmological and galactic bursts, for various assumptions
about the strength of the magnetic field and the particle acceleration
mechanisms in the shocks. The spectra are evaluated over the whole range from
the IR to $>$ GeV, and are compared with the variety of spectral behavior
reported by BATSE, and with the X-ray and optical constraints. For bursts of
duration $\simg 1\s$ acceptable $\gamma$-ray spectra and $L_x/L_\gamma$ ratios
are readily obtained for 'cosmological' models. Blast waves in galactic models
can produce bursts of similar gamma-ray fluence and duration, but they violate
the X-ray paucity constraint, except for the shorter bursts ($\siml 1\s$). We
discuss the prospects for using O/UV and X-ray observations to discriminate
among alternative models.
