  The electromagnetic (EM) perturbations of the black hole solutions in general
relativity coupled to nonlinear electrodynamics (NED) are studied for both
electrically and magnetically charged black holes, assuming that the EM
perturbations do not alter the spacetime geometry. It is shown that the
effective potentials of the electrically and magnetically charged black holes
related to test perturbative NED EM fields are related to the effective metric
governing the photon motion, contrary to the effective potential of the linear
electrodynamic (Maxwell) field that is related to the spacetime metric.
Consequently, corresponding quasinormal (QN) frequencies differ as well. As a
special case, we study new family of the NED black hole solutions which tend in
the weak field limit to the Maxwell field, giving the Reissner-Nordstr\"{o}m
(RN) black hole solution. We compare the NED Maxwellian black hole QN spectra
with the RN black hole QN spectra.
