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The paper presents genetic-based wavelet networks (GWNs) for fault identification of power transformers. GWNs are three-layer structures, which contain wavelet, weighting and summing layers. Using a genetic-algorithm (GA) based optimisation process, the GWNs automatically tune the network parameters, translation and dilation in the wavelet nodes and the weighting values in the weighting nodes. The GWNs, with global search abilities of the GA and the multiresolution and localisation natures of the wavelets, can identify the complicated relations of dissolved gas contents in transformer oil to corresponding fault types. The proposed GWNs have been tested on the Taipower Company diagnostic records and compared with the fuzzy diagnosis system, artificial neural networks as well as the conventional method. The experimental results reveal that the GWNs have remarkable diagnostic accuracy and require far less construction time than conventional methods.