  Recently there has been a renewed interest in axionic generalization of
electrodynamics due to its application to topological insulators. A low-energy
electromagnetic response of these exotic materials was proposed to be described
by an axionic term in the Lagrangian. Motivated by this it is of interest to
study various aspects of axionic electrodynamics and analyze the universal
features of the axionic effects. Here we discuss the axionic modification of
generalized electrodynamics with a Lagrangian being an arbitrary function of
two electromagnetic invariants. Surprisingly, the qualitative characteristics
of the major axionic effects known in the Maxwell theory happen to be
independent of the exact type of the nonlinear Lagrangian and are uniquely
fixed by the form of the axionic term.
