**Asymptotic Estimates for a Nonlinear Acceleration Method of Fourier Series**

Nonlinear acceleration method of Fourier series based on Pade approximation is investigated (see also [12]). Asymptotic estimates of approximation error is represented and comparison with known Bernoulli-acceleration method is given. It is shown that acceleration executes by the quasipolynomials. In an important particular case an obvious form of quasipolynomials is represented.