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The expressions for the quasinormal modes (QNMs) of black holes withnonlinear electrodynamics, calculated in the eikonal approximation, arepresented. In the eikonal limit QNMs of black holes are determined by theparameters of the circular null geodesics. The unstable circular null orbitsare derived from the effective metric that is the one obeyed by light raysunder the influence of a nonlinear electromagnetic field. As an illustration wecalculate the QNMs of four nonlinear electromagnetic black holes, two singularand two regular, namely from Euler-Heisenberg and Born-Infeld theories, forsingular, and the magnetic Bardeen black hole and the one derived by Bronnikovfor regular ones. Comparison is shown with the QNMs of the linearelectromagnetic counterpart, their Reissner-Nordstr\"{o}m black hole.

Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics