This paper presents a method for monitoring power system dynamic stability using the Kohonen neural-net. As far as the eigenvalue calculation is concerned in power system dynamic stability studies, the QR method is widely spread due to the high accuracy. However the method has a drawback that the computational efforts are required as the size of systems increases. Also, the S-matrix method is quite attractive in a sense that the method focuses on the most critical eigenvalue. However, the method has numerical problems in evaluating the most critical eigenvalue. The proposed method makes use of the mapping of the eigenvalue that allows to regard the absolute value of the most critical eigenvalue as a quantitative dynamic stability index. In this paper, the Kohonen neural-net is used to estimate the index. The neural-net has the following advantages: (1) simple algorithm without the teacher's signal; (2) effectiveness for classifying input data; (3) easiness to visually understand classification of input data due to two-dimensional mapping of output neurons. The effectiveness of the proposed method is demonstrated in a three-machine nine-node system.