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In this article, we investigate partially truncated correlation functions(PTCF) of infinite continuous systems of classical point particles with pairinteraction. We derive Kirkwood-Salsburg-type equations for the PTCF and writethe solutions of these equations as a sum of contributions labelled by certainforests graphs, the connected components of which are tree graphs. Wegeneralize the method introduced by R.A. Minlos and S.K. Poghosyan (1977) inthe case of truncated correlations. These solutions make it possible to derivestrong cluster properties for PTCF which were obtained earlier for lattice spinsystems.

Correlation of clusters: Partially truncated correlation functions and their decay