A non-linearly damped single-degree-of-freedom (s.d.o.f.) system under broadband random excitation is considered. A procedure for in-service identification of the damping characteristic from measured stationary response is described. The procedure is based on the stochastic averaging method. The explicit analytical solution is obtained for the integral equation, which relates the desired damping characteristics to the apparent force in the shortened equation for the slowly varying response amplitude, and thus to the measured probability density of the amplitude. The approach is of a non-parametric nature, which makes it convenient for testing hypotheses of damping mechanisms from measured random vibration data. Extensive results of numerical tests for the procedure are presented.