  We derive the equations for the odd and even parity perturbations of coupled
electromagnetic and gravitational fields of a black hole with an electric
charge within the context of general nonlinear electrodynamics. The Lagrangian
density is a generic function of the Lorentz invariant scalar quantities of the
electromagnetic fields. We include the Hodge dual of the electromagnetic field
tensor and the cosmological constant in our calculations. For each type of
parity, we reduce the system of Einstein field equations coupled to nonlinear
electrodynamics to two coupled Schr\"odinger-type wave equations, one for the
gravitational field and one for the electromagnetic field. The stability
conditions in the presence of the Hodge dual of the electromagnetic field are
derived.
