Abstract Vibratory systems subjected to a stationary random external excitation and having random uncertainties in parameters are analyzed. Some quantities characterizing the quality of such systems (quality measures) are defined and evaluated; they are, for example, the average number of level crossings, the average number of maxima, and the departure from normality. The effects of random uncertainty in system parameters on the quality measures are investigated (analytically and numerically) via conditioning. This means that first the conditional quantities (obtained for fixed parameters) are used and then integration with respect to the appropriate distribution is performed. The analysis includes also a discussion of the quality predictions for systems subjected to a random excitation with an exponential correlation by considering a system with an “equivalent” white noise excitation.