Mixed-signal systems combine analog and digital signal processing in one overall design that should be integrated as a single system on chip. At system level, the separation into isolated subsystem representations for analog and digital parts needs to be overcome by a unified formalism that can handle any mix of continuous-time, discrete-time, and hybrid systems. A second driving force in our contribution is that, with decreasing circuit size, nonlinear effects become increasingly prominent. Therefore, several aspects of a consistent theory of nonlinear dynamical systems with mixed-signal domains have been developed. It is based on an extension of the Volterra series approach to the representation of fading-memory systems. We will present novel mixed-domain representations, both in the time and frequency domains, and we develop simple results for system composition. For illustration purposes, we discuss analogto- digital conversion, digital-to-analog conversion, and the digital cancellation of a (nonlinear) analog echo path.