The describing function (DF) method offers a useful a way to analyse the stability of control systems with separable nonlinearities and recently it has been applied to systems with either parametric or norm-bounded perturbations. Here, DFs are employed in an even more general setting, i.e. both types of uncertainty are allowed to enter the system. Furthermore, the high frequency dynamics neglected by the DF technique are also incorporated into the system description. Exploiting some well known results from the robust control literature, computationally tractable stability criteria are derived. Two numerical examples are provided to illustrate the various aspects of these new tools which are, of course, subject to the usual errors and the restrictions of the DF method.