We discuss the evolution of cosmological gamma-ray burst remnants, con
sisting of the cooling and expanding fireball ejecta together with any
swept-up external matter, after the gamma-ray event. We show that sig
nificant optical emission is predicted, which should be measurable for
timescales of hours after the event, and in some cases radio emission
may be expected days to weeks after the event. The flux at optical, X
-ray, and other long wavelengths decays as a power of time, and the in
itial value of the flux or magnitude, as well as the value of the time
-decay exponent, should help to distinguish between possible types of
dissipative fireball models.