A dynamically stable associative learning neural network system include a plurality of synapses (122,22-28), a non-linear function circuit (30) and an adaptive weight circuit (150) for adjusting the weight of each synapse based upon the present signal and the prior history of signals applied to the input of the particular synapse and the present signal and the prior history of signals applied to the input of a predetermined set of other synapses. An embodiment of a conditional-signal neuron circuit (100) receives input signals from conditional stimuli and an unconditional-signal neuron circuit (110) receives input signals from unconditional stimuli. A neural network (200) is formed by a set of conditional-signal and unconditional-signal neuron circuits connected by flow-through synapses to form separate paths between each input (215) and a corresponding output (245). In one embodiment, the neural network (200) is initialized by varying the weight of the input signals from conditional stimuli, until a dynamic equilibrium is reached.