A large class of non-linear dynamic adaptive systems such as dynamic recurrent neural networks can be very effectively represented by Signal-Flow-Graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple one-input one-output transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often use d for qualitative description rather than for rigorous representation and computational purposes. Following an approach originally developed by A.Y. Lee for continuous-time systems based on the concept of adjoint graph, a new algorithm to estimate the derivative of the output with respect to an internal parameter was recently proposed by some of the authors for discrete-time systems. This paper extends further this approach to multirate digital systems, which are nowadays widely used. The new method can be employed for gradient-based learning of general multirate circuits, such as new “multirate” neural networks.