i. The problem of the distribution function of a system with a finite number of levels that interacts with a thermal reservoir and with an external harmonic force arises in the solution of many problems in physics. As examples, we can mention systems that consist of atoms or molecules in the field of a laser wave, the particles existing in a solid or gas that play the role of the thermal reservoir. Many studies have been devoted to the solution of such problems [i-ii]. In many studies, the treatment is restricted to twoand threelevel systems (see, for example, [2]). The anharmonic oscillator is often investigated by means of perturbation theory, the correction to the harmonic potential (the anharmonicity parameter) being regarded as a small quantity [3-6]. In [7,8], nonlinearity is taken into account only in the form of a dependence of the oscillator vibration frequency on the level number, ~(n), and the distribution function is found by means of the quasiharmonic approximation, i.e., the solution for a harmonic oscillator with the frequency replaced by the dependence ~(n). These studies do not take into account higher harmonics in the solution, and this is equivalent to taking into account transitions only between neighboring levels. The nondiagonal elements of the density matrix are also not taken into account, so that the original equation for the density matrix reduces to the solution of the system of balance equations for the populations.