  The effects of highly relativistic spin-gravity coupling in the
Schwarzschild-de Sitter background which follow from the Mathisson-Papapetrou
equations are investigated. The dependence of gravitoelectric and
gravitomagnetic components of gravitational field on the velocity of an
observer which is moving in Schwarzschild-de Sitter's background is estimated.
The action of gravitomagnetic components on a fast moving spinning particle is
considered. Different cases of the highly relativistic circular orbits of a
spinning particle which essentially differ from the corresponding geodesic
orbits are described.
