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Superconducting materials are known to exhibit nonlinear effects and to produce harmonic generation and intermodulation distortion in superconductive circuits. In planar structures, these nonlinearities depend on the current distribution on the strip which is mainly determined by the structure of the device. This paper investigates the current distribution at the step-in-width discontinuity in superconducting microstrip transmission lines, which is computed by a numerical approach based on a 3-D finite-element method. This current distribution is used to obtain the parameters of the nonlinear circuit model for the superconducting microstrip step-in-width discontinuity. The proposed equivalent nonlinear circuit can be solved using the harmonic balance method. Examples of two superconducting structures which contain the steps in width are given and validated by comparison with electromagnetic full-wave results. The proposed model can be used for effective optimization of the superconducting microwave filter resonators in order to minimize their nonlinear distortions.