The properties of the higher-order autocorrelation functions of pseudorandom signals based on m sequences are shown to depend on the existence of linear relationships between members of the m sequence and the way in which the m sequence is mapped into the pseudorandom sequence of real numbers. From the results presented, the autocorrelation functions of any order may be determined analytically for such signals. The particular properties of the autocorrelation functions of pseudorandom signals derived by symmetrical mapping from p-level m sequences are described, and the important case of the 4th-order autocorrelation functions of these signals is discussed in detail and illustrated by an example.