Three different, linear, three-site binding models are presented for the binding of proteins, such as a repressor, to DNA. The first model assumes that the DNA is rigid and all correlations between the Ligands are due to direct ligand-ligand interactions. In the second and third models conformational changes in the DNA are induced by the binding process. In these models we find both direct and indirect correlations between the ligands. Examination of the indirect correlation reveals two characteristic features that, in general, are negligible in the direct correlation. (1) Long range correlation, between nonadjacent sites. (2) Nonadditivity of the triplet correlations. It is shown that these two features cannot be neglected in the indirect correlations. The arguments for explaining these features are similar to those which explain long range and nonadditivies of correlations in the liquid state. (C) 1997 American Institute of Physics. [S0021-9606(97)52046-0].