The transient analysis for a step input to a two-winding transformer is considered. The controlling differential equations are cast in a form amenable to a singular perturbation method. The method of obtaining series solutions corresponding to zeroth- and first-order approximations is described, and several salient features are brought out clearly. An algorithm is given to indicate the various steps involved in the application of the method. Results are obtained for typical numerical values and it is seen that the series solution becomes closer to the exact solution as the order of approximation is increased. An error criterion based on the integral-squared-error is introduced and the variation of this error with the coefficient of coupling of the transformer is examined.