If gamma-ray bursts originate at cosmological distances, as strongly i
ndicated by the results from BATSE on the Compton Gamma-Ray Observator
y (CGRO), then ultrarelativistic ejecta are the likely consequence of
the highly super-Eddington luminosity of the sources. If the energy in
jection rate varies with time, then the Lorentz factor of the wind als
o varies, and the shells of ejected matter collide with each other. Th
e collisions between baryons produce pions which decay into high-energ
y photons, electron positron pairs, and neutrino pairs. The bulk Loren
tz factor of approximately 300 is required if our model is to be compa
tible with the observed millisecond variability. The strongest gamma-r
ay bursts are observed to deliver approximately 10(-4) ergs cm-2 in 10
0-2000 keV photons. In our scenario more energy may be delivered in a
neutrino burst. Typical neutrinos may be approximately 30 GeV if the p
rotons have a Maxwellian energy distribution, and up to is similar to
TeV if the protons have a power-law distribution. Such neutrino bursts
are close to the detection limit of the DUMAND II experiment.