  We investigate the hydrodynamic evolution of Gamma--Ray Burst (GRB) remnants
at late times (>> 1 year), by extending the standard fireball model into the
nonrelativistic Sedov--Taylor regime. We calculate the associated synchrotron
luminosity as a function of remnant age. The radio luminosity of old remnants
depends strongly on the power-law index p= (dlogN/dlogE) of the kinetic energy
distribution of shock-accelerated electrons. In addition, the detection
probability of remnants in nearby galaxies depends on the GRB rate in the local
universe. We predict that if p<2.6 and the BATSE-calibrated GRB rate per
comoving volume is independent of redshift (despite the strong evolution in the
cosmic star formation rate) then the VLA can discover a 10^3 years-old GRB
remnant in the Virgo cluster. Nearby GRB remnants could be searched for and
resolved at radio frequencies, and then identified as distinct from supernova
remnants based on the detection of the extended emission of high-ionization
lines in follow--up optical observations.
