[en] Electron motion in a real nonhomogeneous field of a spiral ondulator is considered. The system singular points, equilibrium trajectories, are determined. It is shown that one of the two trajectories corresponding to the greater radius is unstable that particularly defines the total (nonlinear) ondulator acceptance tending to zero in a minimum magnetic field. The frequencies of small normal oscillations near the stable orbit are found. The notion of radiative acceptance is introduced as an area of the phase space initial values, within its bouns the ondulator focusing properties and finite beam emittance do not perturb the ondulator radiation spectrum. A formula for radiative acceptance true for any fields greater than the minimum one is determined. Restrictions for free electron resonator laser related with radiative acceptance smallness are discussed