  In this paper analytical solutions of the Mathisson-Papapetrou equations that
describe nonequatorial circular orbits of a spinning particle in the
Schwarzschild-de Sitter background are studied, and the role of the
cosmological constant is emphasized. It is shown that generally speaking a
highly relativistic velocity of the particle is a necessary condition of motion
along this type of orbits, with an exception of orbits locating close to the
position of the static equilibrium, where low velocities are possible as well.
Depending on the correlation between the spin orientation of the particle and
its orbital velocity some of the possible nonequatorial circular orbits exist
due to the repulsive action on the particle caused by the spin-gravity coupling
and the others are caused by the attractive action.Here values of the energy of
the particle on the corresponding orbits are also analyzed.
