Influence of long-range interactions between ligands bound to DNA molecule on the character of their adsorption is studied using computer modeling. For this investigation, two calculation procedures are developed. They are based upon the method of the free energy minimum and on the partition function method. The both procedures demonstrate that in the case of a strong enough attraction between all the bound ligands their binding to DNA has the character of phase transition of the first kind. There is a break in the binding curve c(c_o) where c - relative concentration of bound ligands, c_o - molar concentration of free ligands. The break occurs because there is an interval of central degrees of binding (~50% of the maximum c value) that are prohibited for individual DNA molecules. Such a transition might be caused by some types of DNA condensation. Attraction between the neighboring ligands only, adjacent or/and separated by double helix regions, does not cause this effect.