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By extending the pulsed recurrent random neural network (RNN) discussed in Gelenbe (1989, 1990, 1991), we propose a recurrent random neural network model in which each neuron processes several distinctly characterized streams of "signals" or data. The idea that neurons may be able to distinguish between the pulses they receive and use them in a distinct manner is biologically plausible. In engineering applications, the need to process different streams of information simultaneously is commonplace (e.g., in image processing, sensor fusion, or parallel processing systems). In the model we propose, each distinct stream is a class of signals in the form of spikes. Signals may arrive to a neuron from either the outside world (exogenous signals) or other neurons (endogenous signals). As a function of the signals it has received, a neuron can fire and then send signals of some class to another neuron or to the outside world. We show that the multiple signal class random model with exponential interfiring times, Poisson external signal arrivals, and Markovian signal movements between neurons has product form; this implies that the distribution of its state (i.e., the probability that each neuron of the network is excited) can be computed simply from the solution of a system of 2Cn simultaneous nonlinear equations where C is the number of signal classes and n is the number of neurons. Here we derive the stationary solution for the multiple class model and establish necessary and sufficient conditions for the existence of the stationary solution. The recurrent random neural network model with multiple classes has already been successfully applied to image texture generation (Atalay & Gelenbe, 1992), where multiple signal classes are used to model different colors in the image.