Artificial models of biological neural networks can learn from examples and generalize from what they learn, i.e., the learning in them is not rote. This distinctive capability makes them particularly attractive for use as neurocomputing structures in pattern recognition, control, and other complex signal processing tasks. Accordingly, considerable effort is being devoted to the incorporation of the neural paradigm in man-made systems. An important question, encountered in implementation of neurocomputers with adaptive learning ability in photonic hardware, is how to effectively realize programmable nonvolatile analog connection (synaptic) weights between neurons of the network (this incidentally is also an issue in electronic hardware implementation of neural networks). In this paper we consider electron trapping materials (ETMs), a class of infrared stimulable phosphors, as a possible candidate for achieving this goal. We will describe a moderate-sized photonic learning machine, presently under construction, in which the connection weights between neurons, stored in an ETM panel, can be incremented or decremented optically under computer control during learning then frozen in place by means of a novel electronic fixing scheme to form a nonvolatile associative memory. Unique features of several specialized components being used in the machine are also described.