Summary: The paper is devoted to the study of approximations by Fejér means of Fourier series on one system of Chebyshev-Markov algebraic fractions on classes \(MH^{(\gamma)}[-1,1],\gamma\in[-1,1]\), of functions satisfying Lipschitz condition of order \(\gamma\) with a constant \(M\) on a segment \([-1,1]\). The previously known works relating to the studies of asymptotically exact upper bounds of deviations of polynomial Fejér means on Lipschitz classes, as well as some rational methods of approximation are given. Asymptotically exact upper bounds of deviations of sequences of Fejér means of rational Fourier-Chebyshev series on classes \(MH^{(\gamma)}[-1,1],\gamma\in[-1,1]\) are established.