We describe a search for X-ray afterglows from gamma-ray bursts using the R
OSAT all-sky survey (RASS) data. If the emission in the soft X-ray band is
significantly less beamed than in the gamma-ray band, we expect to detect m
any afterglows in the RASS. Our search procedure generated 23 afterglow can
didates, where about 4 detections are predicted. However, follow-up spectro
scopy of several counterpart candidates strongly suggests a flare star orig
in of the RASS events in many, if not all, cases. Given the small number of
events we conclude that the ROSAT survey data are consistent with comparab
le beaming angles in the X-ray and gamma-ray bands. This result is perhaps
not surprising, given that the data constrain the relative beaming fraction
only within a few hours of the burst. However, models predicting a large a
mount of energy emerging as a nearly isotropic X-ray component of the early
afterglow are severely constrained by the ROSAT data. In particular, a so
far undetected class of "dirty fireballs" and delayed "rebursts" are constr
ained.