In this paper, we present a continuous time version of a differential Hebbian learning algorithm for pulsed neural systems with non-linear synapses. We argue that future analogue integrated implementations of artificial neural networks with on-chip learning must take as a starting point the basic properties of the technology. In particular asynchronous and inherently offset free, simple circuit structures must be used. We argue that unsupervised type learning schemes are most natural for analogue implementations and we seek inspiration from psychobiology to derive a learning scheme suitable for adaptive pulsed VLSI neural networks. We present simulations on this new learning scheme and show that it behaves as the original drive-reinforcement algorithm while being compatible with the technology. Finally, we show how the important weight change circuit is implemented in CMOS.