  The classical H. Poincar\'{e} Center-Focus problem asks about the
characterization of planar polynomial vector fields such that all their
integral trajectories are closed curves whose interiors contain a fixed point,
a {\em center}. This problem can be reduced to a center problem for some
ordinary differential equation whose coefficients are trigonometric polynomials
depending polynomially on the coefficients of the field. In this paper we show
that the set of centers in the Center-Focus problem can be determined as the
set of zeros of some continuous functions from the moments of coefficients of
this equation.
