The paper details the problem of transient stability in electrical power systems and divides the methods used to date into four categories. These categories, with the relevant literature, are briefly reviewed.The paper then describes the theory, method of construction and mode of operation of an automatic step-by-step computer for power-system swing curves; the machine has facilities for two generators only but may be extended in scope by the addition of equipment similar to that already employed. The limitations of this machine are discussed and a direct-analogue method for use with the generator units of a network analyser is then described.The procedure for calibration of the direct analogue is given, and difficulties in the setting up of the analogues of damping power and inertia constant are mentioned. Comparison of the results of a simple swing-curve problem by integraph, step-by-step and analogue appears at the end of the paper.Automatic generator-unit operation on a network analyser is possible with this type of direct-analogue equipment.