Abstract A new generalization of the Ornstein-Zernike equation for the functions describing equilibrium correlations between two groups of particles is proposed. The generalized direct correlation functions for two groups of particles are introduced, and the integral equations relating these functions to “full” correlations are derived. The derivation is based on diagrammatic analysis of the correlation functions. As an analogue of a cutting (nodal) vertex in the standard analysis leading to the Ornstein-Zernike equation we consider now a cutting set of vertices. Possible applications of the proposed formalism to the actual calculation of three- and four-particle equilibrium correlation functions are indicated.