V.M.Lipunov 
, K.A.Postnov ,
M.E.Prokhorov 
,
I.E.Panchenko 
,
and H.E. Jorgensen 
Faculty of Physics, Moscow University, 117234 Moscow, Russia
Sternberg Astronomical Institute, Moscow University,
119899 Moscow, Russia
Astronomical Observatory, Ostervoldgade 3, DK-1350 Copenhagen,
Denmark
Evolution of the coalescence rate of double neutron stars (NS)
and neutron star - black hole (BH) binaries are computed for
model galaxies with different star formation rates. Assuming
gamma-ray bursts (GRB) to originate from NS+NS or NS+BH merging
in distant galaxies, theoretical 
- 
distributions for
gamma-ray bursts (GRB) are calculated for the first
time taking the computed merging rates into account.
We use a flat cosmological model ( 
) with different
values of the cosmological constant 
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
exising BATSE sensitivity limit. The most important parameter
in fitting the 2nd BATSE catalogue is the initial redshift of
star formation, which is found to be 
depending on a
poorly determined average spectral index of GRB.
- distribution and 
-test.