  We study the process of resonant generation of high-order harmonics in a
closed cavity in the model of vacuum nonlinear electrodynamics. Concretely, we
study the possibility of resonant generation of the third harmonic induced by a
single electromagnetic mode in a radiofrequency cavity, as well as resonant
generation of a combined frequency mode induced by two pump modes ($\omega_1$
and $\omega_2$). We explicitly show that the third harmonic as well as the
$2\omega_1+\omega_2$ combined frequency mode are not resonantly amplified,
while the $2\omega_1-\omega_2$ signal mode is amplified for certain cavity
geometry. We discuss the process from the point of view of quantum theory.
