This paper extends in a simple way the classical absolute stability Popov criterion to multivariable systems with delays and with time-varying memoryles- s nonlinearities subject to sector conditions. The proposed sufficient conditions are expressed in the frequency domain, a form well-suited for robustness issues, and lead to simple graphical interpretations for scalar systems. Apart from the usual conditions, the results assume basically a generalized sector condition on the derivative of the nonlinearities with respect to time. Results for local and global stability are given, the latter concerning in particular the linear time-varying ones. For rational transfers, the frequency conditions are equivalent to some easy-to-ch- eck Linear Matrix Inequalities: this leads to a tractable method of numerical resolution by approximation. As an illustration, a numerical example is provided.