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In the paper a new fault diagnosis-oriented neural network and a diagnostic method for localization of parametric faults in Analog Electronic Circuits (AECs) with tolerances is presented. The method belongs to the class of dictionary Simulation Before Test (SBT) methods. It utilizes dictionary fault signatures as a family of identification curves dispersed around nominal positions by component tolerances of the Circuit Under Test (CUT). A neural network based classifier with a new Two-Center Ellipsoidal Basis Functions (TCEBFs) is used for fault signature classification. The TCEBF classifier is more robust against component tolerances and multiple parametric faults in comparison with conventional Radial/Ellipsoidal Basis Function (RBF/EBF) neural networks. This article presents a description of the proposed diagnostic method, the construction procedure of the TCEBF, the architecture of the fault classifier and simulation results obtained for the low-pass analog filter.