  We report on a search for X-ray afterglows from gamma-ray bursts using the
ROSAT 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 many
afterglows in the RASS. Our search procedure generated 23 afterglow candidates,
where about 4 detections are predicted. Follow-up spectroscopy of several
counterpart candidates strongly suggests a flare star origin of the RASS events
in many, if not all, cases. Given the small number of events we conclude that
the data are consistent with comparable beaming angles in the X-ray and
gamma-ray bands. Models predicting a large amount of energy emerging as a
nearly isotropic X-ray component, and a so far undetected class of ``dirty
fireballs'' and re-bursts are constrained.
