We consider the light Doppler effect within the framework of our absolute spacetime theory, which proceeds from the aether conception for light propagation. We show that for the cases of “observer at rest, source moving” and “source at rest, observer moving” the formulas for the received frequency are the same, but the formulas for the wavelength are different. This is in a drastic contradiction with the formulas given by contemporary physics, which proceeds from the principle of relativity. Our recently performed (...) “coupled-mirrors” experiments show that only our formulas can adequately describe physical reality. The experiment for the measurement of the transverse light Doppler effect proposed by us in another paper is reconsidered and we point out how it can be realized as a compensation experiment. The so-called “rotor” and “rotor-rotor” experiments are analyzed. We show why the rotor experiment carried out with the aim of establishing an aether drift has failed to give any positive result. (shrink)