More than twenty years after their discovery,1the nature of gamma‐ray burst sources (GRBs) remains mysterious. The remarkable results from BATSE experiment aboard the Compton Observatory show however that most of the sources of gamma‐ray bursts cannot be distributed in the galactic disc. The possibility that a small fraction of sites of gamma‐ray bursts is of galactic disc origin cannot however be excluded. We point out in this paper that large numbers of neutron–star binaries with orbital periodsP∼10 hr and M dwarf companions of mass ∼0.2–0.3 M⊙are a natural result of the evolution of low‐mass x‐ray binaries (LMXBs). The numbers and physical properties of these systems suggest that some gamma‐ray burst sources may be identified with this endpoint of LMXB evolution. We suggest an observational test of this hypothesis.