In this work we delineate the physical picture for the propagation of electromagnetic oscillations in a moving plasma. We present calculations devoted to describing the dispersion features of the radiation that propagates within a magnetoactive plasma. Both classical and relativistic treatments have been employed. We have concluded that if the outflow is moving with small velocities, the general motion of the plasma does not affect the propagation of transverse electromagnetic waves. The waves are refracted according to the ordinary refraction law deduced for non-moving magnetoactive plasmas. The global movement does not change the dispersion relations, and the shapes of the corresponding curves remain unaltered. In the relativistic formulation, we have derived the equations that determine the electromagnetic wave spectrum for a moving magnetoactive plasma. In this case, it is found that the flow velocity affects the plasma dispersion properties and is responsible for new dispersion branches: transverse and longitudinal perturbations. The ordinary and extraordinary electromagnetic modes are modified and described by dispersion relations whose points of resonance are also in explicit dependence on the plasma velocity. Furthermore, the relativistic motion causes the split of electromagnetic modes into two independent waves that propagate at different rates. This effect is remarkable for highly relativistic velocities. The results presented in this work may be applied in order to incorporate suitable corrections to the dispersion models, developed to explain the anomalous features of observed lines or continuum radiation, associated with astrophysical relativistic outflows which are present in gamma-ray bursts, blazars, relativistic jets in AGNs (active galactic nuclei), quasars and microquasars.