The problem of joint data processing from ground-based gravitational and neutrino detectors is considered in order to increase the detection efficiency of collapsing objects in the Galaxy. The development of the “neutrino-gravitational correlation” algorithm is carried out within the framework of the theory of optimal filtration as applied to the well-known OGRAN and BUST facilities located at the BNO INR RAS. The experience of analyzing neutrino and gravitational data obtained during the outburst of supernova SN1987A is used. Sequential steps of the algorithm are presented; formulas for estimating the statistical efficiency of a two-channel recorder are obtained.