  A new type of collective electromagnetic excitations, namely surface
polaritons (SP) --- in a 2D electronic layer in a high magnetic field under
Quantum Hall Effect (QHE) conditions is predicted. We have found the spectrum,
damping, and polarization of the SP in a wide range of frequencies $\omega$ and
wavevectors $\bf k$. It is shown that near the Cyclotron Resonance (CR)
($\omega\sim\Omega=\displaystyle eB/mc$) the phase velocity of the SP is
drastically slowed down and the group velocity undergoes fundamental steps
defined by the Fine Structure Constant $\alpha=e^2/\hbar c$. In the vicinity of
a CR subharmonic ($\omega\sim 2 \Omega$) the negative (anomalous) dispersion of
the SP occurs. The relaxation of electrons in the 2D layer gives rise to a new
dissipative collective threshold-type mode of the SP. We suggest a method for
calculating the kinetic coefficients for the 2D electronic layer under QHE
condition, using the Wigner distribution function formalism and determine their
spatial and frequency dispersion. Using this method we have calculated the
line-shape of the CR and the d.c. conductance under the QHE condition, which
are in good agreement with experimental data.
