  A comparative analysis of the Mathisson-Papapetrou and Pomeransky-Khriplovich
equations is presented. Motion of spinning particles and their spins in
gravitational fields and noninertial frames is considered. The angular velocity
of spin precession defined by the Pomeransky-Khriplovich equations depends on
the choice of the tetrad. The connection of such a dependence with the Thomas
precession is established. General properties of spin interactions with
gravitational fields are discussed. It is shown that dynamics of classical and
quantum spins in curved spacetimes is identical. A manifestation of the
equivalence principle in an evolution of the helicity is analyzed.
