Reliable fault diagnosis and potential remaining useful life (RUL) predication before the occurrence of fatal failure in machinery is critical for improving productivity and reducing maintenance cost. However, the existing physics heuristics and neural networks based methods face difficulties to treat such two issues simultaneously. This paper proposes a novel Network of Extreme Learning Machines (N-ELM) framework, which is a hybrid model of classification and regression for multiple faults diagnosis and RUL predication. The N-ELM consists of a set of ELMs as the nodes of the learning network, which forms a 'generalized' structure with fault detection and RUL forecasting functions. By exploiting the advantages of ELM superb efficiency in regression, the error statistics based robust AdaBoost.RT based ELM framework (RAE-ELM) with self-adaptive threshold mechanism is applied to improve the accuracy of RUL predication. The uniform network of multi-functioning ELMs enable classify fault types and predicate their corresponding RUL concurrently with outperformed accuracy and efficiency. The superior performance of the proposed hybrid framework and supporting techniques are validated using vibration monitoring dataset collected from rotating machinery in the field.