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A state-space technique (SST) for the computation of electromagnetic transients on transmission lines with nonlinear components is presented. State equations for the nonlinear system are derived and these equations are converted to a set of algebraic equations using the trapezoidal rule of integration. A state-space formulation and numerical solution steps are described. To show the validity of the method proposed, two illustrative examples are given. In the first example, lightning surges on a single-phase with a corona are analysed. The effect of the presence of a surge arrester is investigated in the second example. The results obtained using the state-space technique are compared with those obtained using the electromagnetic transients program (EMTP) and with experimental results available in the literature. The proposed method is accurate, numerically stable and suitable for the computation of electromagnetic transients on transmission lines with several nonlinearities.