The postulate of nonequilibrium is at the heart of the second law of thermodynamics. According to this postulate, there is a real property of matter – “nonequilibrium,” which characterizes the uneven distribution of matter and motion in space. All processes (reversible and irreversible) can occur only in nonequilibrium systems. As a quantitative characteristic of the nonequilibrium of the system, the maximum work that can be performed during the transition of the nonequilibrium system to the equilibrium state is considered. The only formulation of the second law is given. When real (irreversible) processes occur, the nonequilibrium of the isolated system decreases, and in reversible processes, the nonequilibrium in the system of locally equilibrium subsystems does not change (the increment of one kind of the nonequilibrium entirely compensated by a decrease in the disequilibrium of some other kind). When the system reaches an equilibrium state, the disequilibrium disappears, and all processes cease. The article provides a calculated confirmation of the theoretical provisions of the concept of nonequilibrium and its mathematical apparatus by examples of determining the loss of the nonequilibrium of system when an isothermal mixing of dissimilar gases, and changes of nonequilibrium of system "pure solvent – solution" in the transition of part of the solvent in the solution. The mixing of the same gases leads to the Gibbs paradox, which is also considered in this paper. The concept of nonequilibrium was developed and the quantitative characteristics (measures) of nonequilibrium of the system were introduced allow to study nonequilibrium systems consisting of locally equilibrium subsystems in the sections of classical thermodynamics as simply as individual equilibrium systems.