The operating point of a power system can be defined as a vector whose components are active and reactive power measurements. If the security criterion is prevention of line overloads, the boundaries of the secure domain of the state space are given by the maximal admissible currents of the transmission lines. The application of an artificial neural network, Kohonen's self-organizing feature map, for the classification of power system states is presented. This classifier maps vectors of an N-dimensional space to a 2-dimensional neural net in a nonlinear way, preserving the topological order of the input vectors. Therefore, secure operating points, that is, vectors inside the boundaries of the secure domain, are mapped to a different region of the neural map than insecure operating points. These mappings are studied using a nonlinear power system model. Choice of security criteria and state space are discussed