Evolution of the coalescence rate of double neutron stars (NSs) and neutron star-black hole (BH) binaries are computed for model galaxies with different star formation rates. Assuming gamma-ray bursts (GRBs) to originate from NS + NS or NS + BH merging in distant galaxies, theoretical log N-log S distributions for GRBs are calculated for the first time taking the computed merging rates into account. We use a flat cosmo-logical model (Ω = 1) with different values of the cosmological constant A and under various assumptions about the star formation history in galaxies. The calculated source evolution predicts a 5-10 times increase of the source statistics at count rates 3-10 times lower than the existing BATSE sensitivity limit. The most important parameter in fitting the second BATSE catalog is the initial redshift of star formation, which is found to be z_* = 2-5, depending on a poorly determined average spectral index of GRBs.
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