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Recently the Department of Trade and Industry announced a Pounds 5.7M Neural Computing Technology Transfer Programme. Under this programme the Department of Chemical and Process Engineering at the University of Newcastle and EDS Advanced Technologies Group have launched a Process Monitoring and Control Club. The aim of this Club is to address development and implementation issues in the application of neural networks to problems in the process industries, including process monitoring, fault detection and diagnosis and process optimisation. This paper outlines the procedure followed to develop an artificial neural network, capable of modelling the thermal behaviour of a system for one such application. This application concerns the thermal modelling of a vessel used in a vitrification process. This is the process whereby highly active liquid waste, obtained in the reprocessing of spent nuclear fuel elements is encapsulated in glass for safe and convenient storage.