Relativistic transformation of the frequency of Thomas precession

. We analyze the relativistic transformation of the frequency of the Thomas precession and show that the known expression for this frequency, written for two different inertial observers, disagrees with the Doppler expression for the signal frequency fixed by these observers. We show that this paradox is inherently related to the known Bacry paradox, and both of them are resolved via the statement that the velocity parameter, entering into the expression for the frequency of the Thomas precession, always corresponds to a rotation-free Lorentz transformation between a set of rest frames of a particle with spin, moving along a curved path, and an inertial frame of observation. Some implications of this result are discussed.