  We study quasinormal modes related to gravitational and electromagnetic
perturbations of spherically symmetric charged black holes in nonlinear
electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class
of Lagrangian with higher-order corrections written by the electromagnetic
field strength and its Hodge dual with arbitrary coefficients, and we
parametrize the corrections for quasinormal frequencies in terms of the
coefficients. It is confirmed that the isospectrality of quasinormal modes
under parity is generally violated due to nonlinear electrodynamics. As
applications, the corrections for quasinormal frequencies in Euler-Heisenberg
and Born-Infeld electrodynamics are calculated, then it is clarified that the
nonlinear effects act to lengthen the oscillation period and enhance the
damping rate of the quasinormal modes.
