Neutron star binaries, such as the one observed in the famous binary pulsar PSR 1913+16, end their life in a catastrophic merger event (denoted here NS2M). The merger releases ∼5 1053 ergs, mostly as neutrinos and gravitational radiation. A small fraction of this energy suffices to power γ-ray bursts (GRBs) at cosmological distances. Cosmological GRBs must pass, however, an optically thick fireball phase and the observed γ rays emerge only at the end of this phase. Hence, it is difficult to determine the nature of the source from present observations (the agreement between the rates of GRBs and NS2Ms providing only indirect evidence for this model). In the future a coinciding detection of a GRB and a gravitational-radiation signal could confirm this model.