Two fundamental problems that are frequently encountered in automated machinery monitoring and diagnostics are formulated into their corresponding mathematical problems of clustering and trend analysis. The need for and the efficiency of multiple-index based trend analysis, in both precisely evaluating the current conditions of a machine system using on-line vibration measurements and obtaining a reliable prediction about its future behaviour, are systematically brought out. Neural network solutions to these problems, particularly the solutions using Self-Organizing Maps (SOM) are sought. Statistical parameters of the on-line vibration signal such as peak-to-peak value, absolute mean value, crest factor etc., are used to form the data set depending on the machinery system being monitored and diagnosed. Self-organizing mapping algorithm is then employed to perform the clustering and feature extraction which takes as the input the multi-dimensional data set and provides as the output the condition of the machinery system. Associated one-layer neural network is developed during the process of SOM and the training of this network is performed in an unsupervised learning mode. A new efficient neural network algorithm that has been previously developed by the present authors for multiple-index based regression is adapted to perform the trend analysis of a machine system. Applications of the above neural network algorithms to the condition monitoring and life estimation of both a bearing system as well as a rotor system are fully demonstrated using real-life data.