  It is proposed that gamma-ray bursts are created in the mergers of double
neutron star binaries and black hole neutron star binaries at cosmological
distances. Bursts with complex profiles and relatively long durations are the
result of magnetic flares generated by the Parker instability in a post-merger
differentially-rotating disk. Some bursts may also be produced through
neutrino-antineutrino annihilation into electrons and positrons. In both cases,
an optically thick fireball of size $\sles\ 100$ km is initially created, which
expands ultrarelativistically to large radii before radiating. Several previous
objections to the cosmological merger model are eliminated. It is predicted
that $\gamma$-ray bursts will be accompanied by a burst of gravitational
radiation from the spiraling-in binary which could be detected by LIGO.
