Abstract The Van Hove correlation function Gd(r, t) is expressed, asa sum of function related to definite pairs of particles. These functions are then exactly expressed as functionals of corresponding specific one-particle distribution functions. The crossing relations for the system of functionals are discussed. The general results for a system of N different particles are then adapted to a two-component system and finally to the particular two-component system of one heavy marked particle and a fluid of (N − 1) light identical particles. For the latter case the part of Gd(r, t) related to the pair, the marked heavy particle and a particle of the fluid, is expanded in powers of γ = m − 1 2 1 (m1 is the mass of the marked heavy particle) and in powers of the density of the fluid. Finally this part of Gd is also calculated numerically for a special case of the low-density fluid with a hard-sphere interaction between the marked heavy particle and a fluid particle.