An artificial neural network-based method for evaluating online power system dynamic stability is presented. Using the matrix transformation of the S-matrix method, the absolute value of the most critical eigenvalue in z-plane may be regarded as a power system dynamic stability index. The artificial neural net of Kohonen is used to estimate the index so that computational efforts are reduced and numerical instability problems are avoided. The Kohonen model is based on the self-organization feature mapping (SOFM) technique that transforms input patterns into neurons on the two-dimensional grid. The algorithm used does not require the teacher's signals and is not too complicated, and the resulting mapping makes it visually easy to understand the input pattern. Power system conditions are assigned to the output neurons on the two-dimensional grid with the SOFM technique. Two methods are presented to calculate the estimate index so that an output neuron calls the index corresponding to an input pattern. The linear and nonlinear decreasing function employed at the learning process are compared. The effectiveness of the proposed method is demonstrated.