  We find the forms of the transfer equations for polarized cyclotron radiation
in the atmospheres of compact stars, which are simple enough to allow practical
implementation and still preserve all important physical effects. We take into
account a frequency redistribution of radiation within the cyclotron line as
well as the relativistic and quantum-electrodynamic effects. Our analysis is
valid for the magnetic fields up to $10^{13}$G and for temperatures well below
500keV.} We present and compare two forms of the radiation transfer equations.
The first form, for the intensities of ordinary and extraordinary modes, is
applicable for the compact stars with a moderate magnetic field strength up to
$10^{11}$G for typical neutron star and up to $10^9$G for magnetic white
dwarfs. The second form, for the Stokes parameters, is more complex, but
applicable even if a linear mode coupling takes place somewhere in the
scattering-dominated atmosphere. Analysing dispersion properties of a
magnetized plasma {in the latter case, we describe a range of parameters where
the linear mode coupling is possible and essential.
