Feedforward neural networks are massively parallel computing structures that have the capability of universal function approximation. The most prevalent realisation of neural nets is in the form of an algorithm implemented in a computer program. Neural networks as computer programs lose the inher- ent parallism. Parallism can only be recovered by executing the program on an expensive parallel digital computer. Achievement of the inherent massive parallelism at a lower cost requires direct hardware realisation of the neural net. Such hardware has been developed jointly by QUT and the Heinz Nixdorf Institute (Germany) called the Local Cluster Neural Network (LCNN) chip. But this neural net chip lacks the capability of in-circuit learning or on-chip training. The weights for the analogue LCNN network have to be computed o® chip on a digital computer. Based on the previous work, this research focuses on the Local Cluster Neu- ral Network and its analogue chip. The characteristic of the LCNN chip was measured exhaustively and its behaviours were compared to the theoretical functionality of the LCNN. To overcome the manufacturing °uctuations and deviations presented in analogue circuits, we used chip-in-the-loop strategy for training of the LCNN chip. A new training algorithm: Probabilistic Random Weight Change for the chip-in-the-loop training for function approximation. In order to implement the LCNN analogue chip with on-chip training, two training algorithms are studied in on-line training mode in simulations: the Probabilistic Random Weight Change (PRWC) algorithm and the modified Gradient Descent (GD) algorithm. The circuits design for the PRWC on-chip training and the GD on-chip training are outlined. These two methods are compared for their training performance and the complexity of their circuits. This research provides the foundation for the next version of LCNN analogue hardware implementation.