As new microcontrollers and related processors have become available, it has become possible to create embedded systems for condition monitoring and fault diagnosis (CMFD). This thesis explores how two popular classifiers: the MultiLayer Perceptron (MLP) and Radial Basis Function neural Network (RBFN), can be most effectively employed in embedded CMFD systems.;The design of an embedded CMFD system can be considered to consist of three stages, involving data pre-processing, classification, and post-processing of classifier outputs. The thesis makes contributions to each of these phases as follows.;First, the thesis describes a novel separability analysis method which is able to predict the relative effectiveness of pre-processing techniques. An important aspect of this method is that the separability is derived from a non-parametric analysis: it therefore requires no assumptions to be made about the underlying distribution of the data.;Second, a design methodology is derived that may be used to help the software engineer select between the use of MLP or RBFN classifiers in the CMFD system, depending on the particular system requirements. The design methodology is the result of a comprehensive series of empirical studies. The comparison criteria used are those of particular relevance in embedded CMFD applications. These include classification performance in the presence of unknown faults, with multiple faults, and with limited training data. The criteria also include processor and memory requirements.;Third, the thesis develops a novel technique that allows the user to determine an appropriate threshold for interpreting the outputs of a trained RBFN classifier. Results from two experiments demonstrate that this technique can be used to improve the performance of RBFN classifiers in practical CMFD applications where 'unknown faults' may occur.