a natural generalization of the classical Chebyshev polynomials associated with the root system of the Lie algebra $sl(3)$. These polynomials are called the Chebyshev - Koornwinder polynomials in the following. In [@N27] and [@N31]-[@N33] these ideas were extended to the case of several variable analogues of the other classical polynomials (see also [@N34]). More results can be found in the [@N35; @N37]. We note also the works [@N39]-[@N45] related to the other generalizations of Chebyshev polynomials on the case of several variables.

The purpose of our work consists in the determination of the algebra of the generalized Chebyshev - Koornwinder oscillator and study some properties of this algebra. Considered oscillator-like system, associated with Chebyshev - Koornwinder polynomials (hereinafter ChK-polynomials) [@N28], was defined in the our works [@N46; @N47], based on the scheme proposed in [@N16]. The Chebyshev-Koornwinder oscillator (hereinafter ChK-oscillator) was considered in [@N46] as a union of three oscillators: sectorial, radial and boundary ones. In [@N46] the main attention was paid to the quantum-mechanical aspects of the generalized oscillator while the details of the construction, exact formulas for the ladder operators, and the study of related oscillator algebras were omitted due to space restriction. In [@N47] were obtained differential 