Abstract: A practical system for fault diagnosis should have the following three functions: one with which fault diagnosis can be done very quickly so that the system can find use for fault diagnosis in real time production processes; one with which the training (or learning) of the system and diagnosis for the processes can be carried out simultaneously; and one with which knowledge learned about faults can be accumulated when learning is going on.We focus on how to construct a fault diagnosis system, which is based on neural network. We discuss a new type of neural network, named a linear classifying-reforming neural network and how to train it for fault diagnosis.The linear classifying-reforming neural network system is based on linear learning algorithm. The system consists of classifying sub-network and reforming sub-network. The classifying sub-network does a classification for inputting patterns to be recognized, and at the same time the output results from the network are inputted the reforming sub-network. The reforming sub-network can treat the information from the classifying sub-network and output some reforming patterns related to the recognized patterns. A simple recurrent linear algorithm is adopted for training the system. Because the training is done recurrently and only weights needed to change are adjusted in training, the training can be done very quickly, and the system is able to classify and learn simultaneously. Moreover, the weights of the sub-networks could not be destroyed when training, so that knowledge learned can be accumulated. The use of the linear classifying-reforming neural network is illustrated in incipient fault diagnosis of a chemical reactor.