  Fermi-edge absorption theory predicting the spectrum, A(\omega)\propto
\omega^{-2\delta_0/\pi+\delta^2_0/\pi^2}, relies on the assumption that
scattering phase, \delta_0, is frequency-independent. Dependence of \delta_0 on
\omega becomes crucial near the resonant condition, where the phase changes
abruptly by \pi. In this limit, due to finite time spent by electron on a
resonant level, the scattering is dynamic. We incorporate this time delay into
the theory, solve the Dyson equation with a modified kernel and find that, near
the resonance, A(\omega) behaves as \omega^{-3/4} |\ln \omega|. Resonant
scattering off the core hole takes place in 1D and 2D in the presence of an
empty subband above the Fermi level; then attraction to hole splits off a
resonant level from the bottom of the empty subband. Fermi-edge absorption in
the regime when resonant level transforms into a Kondo peak is discussed.
