The 3D radiative transfer equation for differentially moving media is deriv
ed upon the assumption that the motions are sufficiently slow. Its solution
is then applied to the limiting case of large optical depths, i.e. to the
diffusion approximation. Although the effective extinction for static 1D me
dia has been derived by Rosseland already in 1924, it is for the first time
in this Paper that for moving 3D media with many spectral lines general ex
pressions for radiative quantities are derived in a rigorous way. Given are
simple to use monochromatic as well as wavelength-integrated expressions f
or the flux and the radiative acceleration, and a generalized version of th
e Rosseland mean opacity. The essential effects of the motions upon the rad
iative flux are discussed for the simple case of a single spectral line on
a continuum.