The exact computation, the exact modeling of the propagation of electromagnetic signals through inhomogeneous moving media, is an old theoretical and measuring/data interpretation problem, because in a lot of practical problems, such as the accurate space‐time determination in satellite positioning systems, the occultation measurements, or the accurate tracking of the interplanetary probes, the electromagnetic wave (signal) traverses moving, inhomogeneous media, where the moving velocity of the media and the media itself are inhomogeneous in space, i.e., the Earth's high and low atmosphere, the planetary atmospheres, the interplanetary matter in the inner and outer solar system, etc. In other important cases of electromagnetic wave propagation, as the propagation in inhomogeneous media or the propagation of short impulses (ultrawide‐band (UWB) signals), the application of the method of inhomogeneous basic modes (MIBM) was successful. In this paper it is demonstrated that the application of MIBM in the case of inhomogeneous moving media produces an exact, full‐wave solution of monochromatic or UWB signals propagating through these media. The solutions are valid inside the special relativity.