Conditions are proposed of the availability of the oscillation property in the sense of Yakubovich in a system with a nonlinear nominal portion enclosed by static nonlinear output feedback. A technique is worked out to calculate analytical estimates for the amplitude of oscillations in the system. The relation between estimates for the amplitude of oscillations and the index of excitability of the system with respect to the input is established. Examples are given of the computer modeling for systems of the 2nd and the 3rd order, including Van der Pol and Lorentz systems confirming the applicability of the suggested solutions.