The class of nonlinear time-varying (NLTV) systems includes all possible systems and, hence, is difficult to identify. Still, when the nonlinearities are not too strong then, depending on the application, a linear model might be sufficient for approximating the true response. To quantify the approximation error of the linear model, detecting and quantifying the nonlinear behavior is of key importance. In this paper we propose a fully automated procedure for detecting, classifying and quantifying the nonlinear distortions in the response, possibly subject to a trend, of a specific class of NLTV systems to odd random phase multisine excitations. The result is a measurement of the time-varying frequency response function together with uncertainty bounds due to noise and nonlinear distortions. The user only has to specify four integer numbers: an upper bound on (i) the degree on the time-domain polynomial modelling of the trend, (ii) the degree of the frequency-domain polynomial basis function and (iii) the number of frequency-domain hyperbolic-like basis functions, all used for modeling the output spectrum; and (iv) a quality measure – called degrees-of-freedom – of the noise variance estimate. Guidelines are provided for obtaining reasonable values for these upper bounds.