  The expressions for the quasinormal modes (QNMs) of black holes with
nonlinear electrodynamics, calculated in the eikonal approximation, are
presented. In the eikonal limit QNMs of black holes are determined by the
parameters of the circular null geodesics. The unstable circular null orbits
are derived from the effective metric that is the one obeyed by light rays
under the influence of a nonlinear electromagnetic field. As an illustration we
calculate the QNMs of four nonlinear electromagnetic black holes, two singular
and two regular, namely from Euler-Heisenberg and Born-Infeld theories, for
singular, and the magnetic Bardeen black hole and the one derived by Bronnikov
for regular ones. Comparison is shown with the QNMs of the linear
electromagnetic counterpart, their Reissner-Nordstr\"{o}m black hole.
