It is well known that all the field theories have a property of delay of the interactions. Such are the electromagnetic interaction of charges in vacuum, the interaction of vibrational systems through a medium, the interactions between the particles in a plasma or colloidal systems, etc. The delay of the interactions leads to violation of Newton's third law on the equality of action and reaction , and also it is one of the mechanisms for the irreversible behavior of many-body systems [2,3]. Note that in papers [2,3] neither probabilistic considerations nor the conditions that the number of degrees of freedom in the system is large were used. In this connection, it is of interest to study in detail the mechanisms of the manifestation of retardation in the irreversibility of systems with a small number of degrees of freedom. The simplest case in which the interactions retardation effect can appear is a system consisting of two particles. We define a one-dimensional two-particle oscillator as a system of two particles with identical masses, the interaction between which at rest is described by a potential with a characteristic minimum at a distance L. Let us consider the case of small oscillations of these particles. The retardation of the interaction between the constituents of a two-body oscillator leads to the following effects. 1. Stationary oscillations exist only for a discrete set of equilibrium distances between the particles, determined by the "quantization" condition. The frequencies of all stationary oscillations are the same. 2. If the equilibrium distance L between the particles does not satisfy the "quantization" condition, then there are only non-stationary oscillations in the system. The corresponding oscillations either decay or increase. In both of these cases, the energies of the oscillations are not conserved. 3. The retardations in interactions between the particles performs functions similar to those of a thermodynamic reservoir, which, however, is not something external, but is inextricably linked to the particles. Thus, taking into account the seemingly insignificant but always existing delay in the interaction between the particles leads to a qualitative change in the dynamics of the system of interacting particles, including the phenomenon of irreversibility. Therefore, the classical theory of systems of particles with retarded interactions can be used for a correct microscopic foundation of thermodynamics. The work is supported by the Ministry of Education and Science of Russian Federation within the framework of the project part of the state order (project No.3.3572.2017/PP). REFERENCES  A. V. Ivlev, J. Bartnick, M. Heinen, e.a., Phys. Rev. X, 5(1) (2015) 011035.  A. Yu. Zakharov, M. A. Zakharov. Phys. Lett. A, 380(3) (2016) 365.  A. Yu. Zakharov. Physica A: Stat. Mech. Appl., 473 (2017) 72.