  In many GRB inner engine models the highly relativistic GRB jets are engulfed
by slower moving matter. This could result in different beaming for the prompt
$\gamma$-ray emission and for the lower energy afterglow. In this case we
should expect that some observer will see {\it on-axis orphan afterglows}:
X-ray, optical and radio afterglows within the initial relativistic ejecta with
no preceding GRB; The prompt $\gamma$-ray emission is pointing elsewhere. We
show that the observations of the WFC on BeppoSAX constrain with high certainty
the prompt X-ray beaming factor to be less than twice the prompt $\gamma$-ray
beaming. The results of Ariel 5 are consistent with this interpretation. The
RASS from ROTSE and HEAO-1 constrain the X-ray beaming factor at 400 and 20
minutes after the burst respectively to be comparable and certainly not much
larger than the $\gamma$-ray beaming factor. There is no direct limit on the
optical beaming. However, we show that observations of several months with
existing hardware could result in a useful limit on the optical beaming factor
of GRB afterglows.
