The paper presents an analytical study of the stability of hidden oscillations arising in a 3rd order system with a discontinuous right-hand side. Numerical examples are given to illustrate the correctness of the results obtained. The problem of searching for hidden oscillations in nonlinear systems has been formulated relatively recently, but the study of parasitic oscillations when restrictions are imposed on control or phase variables has been widely discussed in the literature since the implementation of the simplest control algorithms with restrictions. Works in which parasitic oscillations occurred when using a harmonic external force or when limiting linear control with a complex spectrum of corresponding eigenvalues have become widespread. Unlike other works on the study of parasitic oscillations, in [4] a mathematical definition of this mode of operation of a nonlinear system is given. In addition to the definition, the authors also proposed a method for searching for hidden fluctuations based on reducing the system to the Lurie type. Unfortunately, as it was shown in [7], [9], [10], there is a fairly simple class of systems for which this method is not applicable, but at the same time, hidden oscillations and hidden attractors exist in these systems. This article builds on the research started at [10] and is a continuation of the work of [11]. In these works, the problem of stabilizing a third-order integrator using a control with a nested structure of saturation functions was investigated. In [11], a new discontinuous control law is proposed, which makes it possible to construct hidden fluctuations in an analytical form for a closed system. In this paper, it will be proved that the assumptions made about the structure of latent vibrations are a consequence of the occurrence of a sliding mode in a closed system, and the point mapping approach adapted for discontinuous systems by Feigin [2] will be used to study the properties of oscillatory modes. Thus, the purpose of this work is to show that in the studied third-order system with a discontinuous right-hand side, hidden fluctuations arise only due to the occurrence of a stable sliding regime on the switching surface, when determining the Filippov solution.