The paper proposes that gamma-ray bursts (GRBs) are produced during the mergers of double neutron star (NS-NS) and black hole-neutron star (BH-NS) binaries at cosmological distances. The complex profiles and long durations of some bursts are attributed to magnetic flares generated by the Parker instability in a post-merger differentially-rotating disk. Neutrino-antineutrino annihilation is also suggested as a mechanism for some bursts. An optically thick fireball of size less than 100 km is initially created, which expands ultrarelatively and radiates. The model predicts that GRBs will be accompanied by gravitational radiation from the spiraling-in binary, detectable by LIGO. The authors address several objections to the cosmological merger model, including the large optical depth and the Ruderman limit, and provide a qualitative scenario for the production of GRBs in NS-NS and BH-NS binary mergers. They argue that the model can explain the observed properties of GRBs and circumvent many arguments against the cosmological merger model. The scenario predicts that strong GRBs should be accompanied by gravitational wave detections, which could provide valuable information about the bursts' sources.The paper proposes that gamma-ray bursts (GRBs) are produced during the mergers of double neutron star (NS-NS) and black hole-neutron star (BH-NS) binaries at cosmological distances. The complex profiles and long durations of some bursts are attributed to magnetic flares generated by the Parker instability in a post-merger differentially-rotating disk. Neutrino-antineutrino annihilation is also suggested as a mechanism for some bursts. An optically thick fireball of size less than 100 km is initially created, which expands ultrarelatively and radiates. The model predicts that GRBs will be accompanied by gravitational radiation from the spiraling-in binary, detectable by LIGO. The authors address several objections to the cosmological merger model, including the large optical depth and the Ruderman limit, and provide a qualitative scenario for the production of GRBs in NS-NS and BH-NS binary mergers. They argue that the model can explain the observed properties of GRBs and circumvent many arguments against the cosmological merger model. The scenario predicts that strong GRBs should be accompanied by gravitational wave detections, which could provide valuable information about the bursts' sources.