This paper presents an application of Kohonen neural networks to assess the dynamic security of power systems. The dynamic security assessment(DSA) is an important factor in power system operation, but conventional techniques have not achieved the desired speed and accuracy. The critical clearing time(CCT) is an attribute which provides significant information about the quality of the post-fault system behaviour. The function of Kohonen networks is a mapping of the pre-fault system conditions into the neurons based on the CCTs. The power flow on each line is used as the input data, and an activated output neuron has information of the CCT of each contingency. The trajectory of the activated neurons during load changes can be used in on-line DSA efficiently. The applicability of the proposed method is demonstrated using a 9-bus example.