Long-range interaction between all the ligands bound to DNA molecule may give rise to adsorption with the character of phase transition of the first kind (D. Y. Lando, V. B. Teif, J. Biomol. Struct & Dynam. 18, 903-911 (2000)). In this case, the binding curve, c(c_o), is characterized by a sudden change of the relative concentration of bound ligands (_c) at a critical concentration of free (unbound) ligands, c_o=c_ocr, from a low c value to a high one where c_o is molar concentration of free ligands. Such a transition might be caused by some types of DNA condensation or changes in DNA topology. For the study of the conditions necessary for adsorption with the character of phase transition, a calculation procedure based on the method of the free energy minimum is developed. The ligand size and two types of interactions between ligands adsorbed on DNA molecule are taken into consideration: long-range interaction between all the ligands bound to DNA and contact interactions between neighboring ligands. It was found that a) Stronger long-range interaction is required for longer ligands to induce phase transition that is occurred at greater c_ocr values; b) Pure contact interaction between neighboring ligands can not itself initiate phase transition. However contact cooperativity strongly decreases the threshold value of energy of long-range interaction necessary to give rise to the transition.