We present detailed calculations of nonthermal synchrotron and synchrotron
self-Compton (SSC) spectra radiated by blast waves that are energized by in
teractions with a uniform surrounding medium. Radio, optical, X-ray, and ga
mma-ray light curves and spectral indices are calculated for a standard par
ameter set that yields hard GRB spectra during the prompt emission phase. N
o lateral spreading of the blase wave is assumed. Absence of SSC hardenings
in observed GRB X-ray afterglows indicates magnetic held generation toward
equipartition as the blast wave evolves. EGRET detections of 100 MeV-GeV p
hotons observed promptly and 90 minutes after GRB 940217 are attributed to
nonthermal synchrotron radiation and SSC emission from a decelerating blast
wave, respectively. The SSC process will produce prompt TeV emission that
could be observed from GRBs with redshifts z less than or similar to 0.1, p
rovided gamma-gamma opacity in the source is small. Measurements of the tim
e dependence of the 100 MeV-GeV spectral indices with the planned Gamma-ray
Large Area Space Telescope mission will chart the evolution of the SSC com
ponent and test the external shock scenario. Transient optical and X-ray em
issions from misaligned GRBs are generally much weaker than on-axis emissio
ns produced by dirty and clean fireballs that would themselves not trigger
a GRB detector; thus, detection of long-wavelength transients not associate
d with GRBs will not unambiguously demonstrate GRB beaming.