Aims. A solution of the radiative-transfer problem in 3D with arbitrary velocity fields in the Eulerian frame is presented. The method is implemented in our 3D radiative transfer framework and used in the PHOENIX/3D code. It is tested by comparison to our well-tested 1D co-moving frame radiative transfer code, where the treatment of a monotonic velocity field is implemented in the Lagrangian frame. The Eulerian formulation does not need much additional memory and is useable on state-of-the-art computers, even large-scale applications with 1000's of wavelength points are feasible. Methods. In the Eulerian formulation of the problem, the photon is seen by the atom at a Doppler-shifted wavelength depending on its propagation direction, which leads to a Doppler-shifted absorption and emission. This leads to a different source function and a different Lambda{*} operator in the radiative transfer equations compared to the static case. Results. The results of the Eulerian 3D spherical calculations are compared to our well-tested 1D Lagrangian spherical calculations, the agreement is, up to v(max) = 1 x 10(3) km s(-1) very good. Test calculation in other geometries are also shown.