We estimate the frequency of mergers of binary neutron stars and black holes by using a numerical scenario computer program to model the binary star population of the Galaxy. An extrapolation of the estimates shows that, with the gravitational wave detectors now under development, one may hope to detect up to ~ 100 neutron star mergers per year at distances ≤ 200 Mpc. The calculated merger rates based on binary pulsar statistics probably underestimate this detection rate, because of the short lifetimes of most new-born neutron star binaries. The rate of detection of black hole mergers may be comparable to that of neutron star mergers because of the strong dependence of the power of outbursts on the masses of merging objects.