Superconducting materials exhibit an experimentally verified nonlinear dependence with respect to the magnetic field. In this paper, this nonlinearity is taken into account in the evaluation of the attenuation constant in propagating structures of practical usage. Quadratic and cubic nonlinearities are considered, and an iterative numerical procedure is applied to calculate the attenuation constant. The nonlinearity in the penetration depth is also considered. In section 3, some typical structures are investigated. In particular, parallel-plane transmission lines filled by dielectric materials, microstrip lines, and striplines are considered. Comparisons with existing results show that this nonlinear behavior cause significant changes in the attenuation parameters. ¿ 2001 American Geophysical Union