This demo nstrates the use of the reversible jump MCMC algorithm for neural networks. It uses a hierarchical full Bayesian model for neural networks. This model treats the model dimension (number of neurons), model parameters, regularisation parameters and noise parameters as random variables that need to be estimated. The derivations and proof of geometric convergence are presented, in detail, in: Christophe Andrieu, Nando de Freitas and Arnaud Doucet. Robust Full Bayesian Learning for Neural Networks. Technical report CUED/F-INFENG/TR 343, Cambridge University Department of Engineering, May 1999. After downloading the file, type \"tar -xf rjMCMC.tar\" to uncompress it. This creates the directory rjMCMC containing the required m files. Go to this directory, load matlab5 and type \"rjdemo1\". In the header of the demo file, one can select to monitor the simulation progress (with par.doPlot=1) and modify the simulation parameters.