An original approach for describing chemical equilibrium shifts in systems of any physico-chemical nature has been developed. The mathematical expression of the equilibrium principle as formulated by the authors contains, instead of the standard heat and volume changes during a chemical reaction, mixing functions that in some special cases exceed the standard ones. It is shown that in systems with extremely large deviations from ideality (for example, in aqueous solutions of uranyl salts or water-soluble light fullerenes derivatives) the equilibrium shift principle developed by the authors may fundamentally differ from the wellknown Le Chatelier-Brown principle).