  If the efficiency for producing $\gamma$-rays is the same in short duration
($\siml 2$ s) Gamma-Ray Bursts (GRBs) as in long duration GRBs, then the
average kinetic energy of short GRBs must be $\sim 20$ times less than that of
long GRBs. Assuming further that the relativistic shocks in short and long
duration GRBs have similar parameters, we show that the afterglows of short
GRBs will be on average 10--40 times dimmer than those of long GRBs. We find
that the afterglow of a typical short GRB will be below the detection limit
($\siml 10 \microJy$) of searches at radio frequencies. The afterglow would be
difficult to observe also in the optical, where we predict $R \simg 23$ a few
hours after the burst. The radio and optical afterglow would be even fainter if
short GRBs occur in a low-density medium, as expected in NS-NS and NS-BH merger
models. The best prospects for detecting short-GRB afterglows are with early
($\siml 1$ day) observations in X-rays.
