For non-linear Volterra systems which include a non-linear state equation and a general non-linear output function, the system frequency response functions and some related frequency response characteristics are developed and discussed in this study. These new results establish the frequency response functions for this general form of non-linear systems by extending some existing theory, and provide an analytical insight into the relationship between model parameters and frequency response functions, and the relationship between model parameters and the magnitude bound of frequency response functions. Several examples are given to illustrate the new results.