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The paper describes mathematical models suitable for digital simulation of saturated systems. The method takes account of the changing saturation at every instant by using the magnetisation curve. The transient behaviour of the transformer is first studied, and the technique is then extended to cover the case of sudden line-line short circuit of the synchronous machine. Computed values are in good agreement with test results throughout, and a contrast is drawn between the basic simplicity of the method, and the complex problems to which it may readily be applied.