The problem of estimating an unknown multivariate function from on-line vibration measurements, for determining the conditions of a machine system and for estimating its service life is considered. This problem is formulated into a multiple-index based trend analysis problem and the corresponding indices for trend analysis are extracted from the on-line vibration data. Selection of these indices is based on the simultaneous consideration of commonly-observed faults or malfunctions in the machine system being monitored. A neural network algorithm that has been developed by the present authors for multiple-index based regression is adapted to perform the trend analysis of a machine system. Applications of this neural network algorithm to the condition monitoring and life estimation of both a bearing system as well as a gearbox are fully demonstrated. The efficiency and computational supremacy of the new algorithm are established through comparing with the performance of Self-Organizing Mapping (SOM) and Constrained Topological Mapping (CTM) algorithms. Further, the usefulness of multiple-index based trend analysis in precisely predicting the condition and service life of a machine system is clearly demonstrated. Using on-line vibration signal to constitute the set of variables for trend analysis, and employing the newly-developed self-organizing neural algorithm for performing the trend analysis, a new approach is developed for machinery monitoring and diagnostics.