Pseudorandom sequences are series of apparently random numbers generated, for example, by linear or nonlinear feedback shift registers. An important application of these sequences is in spread spectrum communication systems, in which, for example, the transmitted carrier phase is digitally modulated rapidly and pseudorandomly and in which the information to be transmitted is incorporated as a slow modulation in the pseudorandom sequence. In this case the transmitted information can be extracted only by a receiver that uses for demodulation the same pseudorandom sequence used by the transmitter, and thus this type of communication system has a very high immunity to third-party interference. However, if a third party can predict in real time the probable future course of the transmitted pseudorandom sequence given past samples of this sequence, then interference immunity can be significantly reduced.. In this application effective pseudorandom sequence prediction techniques should be (1) applicable in real time to rapid (e.g., megahertz) sequence generation rates, (2) applicable to both linear and nonlinear pseudorandom sequence generation processes, and (3) applicable to error-prone past sequence samples of limited number and continuity. Certain optical processing techniques that may meet these requirements are discussed in this paper. In particular, techniques based on incoherent optical processors that perform general linear transforms or (more specifically) matrix-vector multiplications are considered. Computer simulation examples are presented which indicate that significant prediction accuracy can be obtained using these transforms for simple pseudorandom sequences. However, the useful prediction of more complex pseudorandom sequences will probably require the application of more sophisticated optical processing techniques.