Abstract: Contribution of N.M. Chuiko to the development of the coexistence theory of slag structure. The insufficiency of the previous demonstration for this theory. Further fundamental facts confirming the coexistence theory of slag structure (the facts of crystal chemistry, the difference in electric conductivity of various slags, the liquid miscibility gaps of MeO-SiO₂ bin-nary slags,the peaks on the temperature composition diagram of MeO-SiO₂ binarg slags, the viscosity-composition diagram of CaSiO₃-CaF₂ system, the relation between standard free energy of formation of silicates and mass action concentrations). some examples about the use of the above mentioned theory (eqnilibrum between FeO-Fe₂O₃-SiO₂ and H₂O + H₂,CaO-SiO₂, distribution of sulfur between CaO-MgO-FeO-Fe₂O₃-SiO₂-S and liquid iron).