We discuss the formulation of the radiative transfer equation in the comoving frame. For characteristic velocities larger than ∼ 2000 km s−1 , the effects of advection on the synthetic spectra are non-negligible, and hence they should be included in model calculations. We show that the time-independent or quasi-static approximation is adequate for most astrophysical problems, e.g., hot stars, novae and supernovae. We examine the use of the Sobolev approximation in modelling moving atmospheres, and find that the number of overlapping lines in the comoving frame make the approximation suspect in models that predict both lines and continua. We also discuss the form of the Rosseland mean opacity in the comoving frame, and derive a formula that is easy to implement in radiation hydrodynamics calculations.