  The impact of local space anisotropy on the transverse Doppler effect is
examined. Two types of laboratory experiments aimed at seeking and measuring
the local space anisotropy are proposed. In terms of the conventional special
relativity theory, which treats 3D space to be locally isotropic, the
experiments are of the type of ``null-experiments''. In the first-type
experiments, a feasible Doppler shift of frequency is measured by the
M\"ossbauer effect, with the M\"ossbauer source and absorber being located at
two identical and diametrically opposed distances from the center of a rapidly
rotating rotor, while the $\gamma$-quanta are recorded by two stationary and
oppositely positioned proportional counters. Either of the counters records
only those $\gamma$-quanta that passed through the absorber at the moment of
the passage of the latter near a counter. The second-type experiments are made
using the latest radio physics techniques for generating monochromatic
oscillations and for recording weak signals. The effect expected due to space
anisotropy consists in frequency modulation of the harmonic oscillations coming
to a receiver that rotates at a constant velocity around the monochromatic wave
emitter. In this case the modulation depth proves to be proportional to the
space anisotropy magnitude.
