The analysis of electromagnetic problems with moving objects has many applications: RF Doppler radars, astrophysics, GPS, electromagnetic gyroscopes… This seminar proposes an original and thorough analysis of the behavior of electromagnetic waves in the presence of moving bodies by using the Finite Difference Time Domain (FDTD) method. Movements are implemented by changing positions of the objects at each time step, through the classical FDTD time loop. With this direct approach, time is implicitly absolute and Voigt-Lorentz transformations are not implemented. This technique is suitable for non-relativistic speeds and, thus for most encountered electromagnetic problems, especially in antennas and propagation domain. The numerical aspects that need to be considered are studied. Then, different problems are investigated: moving plane wave source with resistors, moving observation point, moving inclined Partially Reflecting Surface (PRS), moving line source, and moving metallic cylinder illuminated by a plane wave. The results, in terms of Doppler frequency shift and changes in amplitude of the electric field, are compared with those of special relativity which are considered as the references. Some aspects of special relativity are present in the direct FDTD approach, such as the independence of the velocity of electromagnetic wave propagation with the speed of the source and Lorentz local time (with a different physical interpretation). Some of the obtained results agree with special relativity. Other ones are different, but the differences are negligible for non-relativistic speeds. Techniques are proposed for the implementation of relativistic effects. The results obtained with our analysis bring new physical insights into the propagation of waves with moving bodies. In particular, it is shown that the amplitude of the electric field for an ideal plane wave source does not increase with the speed of motion. Moreover, for a moving scattering metallic wire, one can observe a phenomenon similar to shock waves. Other analyzed problems include complex motions (multiple speeds, acceleration, rotation, oscillation), moving airplanes, Michelson-Morley interferometer, Sagnac effect, and Heaviside faster-than-light analysis. Some quantum phenomena (Compton experiment, blackbody radiation) are also studied… Co-sponsored by: INRS, Staracom Room: 6900, Bldg: 800, De La Gauchetière Ouest Bureau, INRS, 6th floor, MONTREAL, Quebec, Canada, H5A 1K6