The Brownian motion in connection to anharmonic oscillations of particles is taken as a basic property associated with a liquid state. The T-g, T-m transitions are discussed in this context. It is shown that consideration of anharmonicity leads to the strong fluctuations in amplitudes and densities, as well as to the coexistence of double values of amplitudes and strong vibrational pulses randomly distributed in a liquid matrix. The analyses of T-g, T-m, or T-B transitions by use of the anharmonic oscillator approach allow us to use similar mathematical tools which are so successfully used in the Voltera-Prigogine type of thermodynamics. In spite of the fact that the anharmonicity effect has already been investigated before, the full impact of ''S'' shaped amplitude hystereses on the partition function is worked out in more detail in the present paper. (C) 1997 American Institute of Physics.