  We study neutrino spin oscillations in gravitational fields. The
quasi-classical approach is used to describe the neutrino spin evolution. First
we examine the case of a weak gravitational field. We obtain the effective
Hamiltonian for the description of neutrino spin oscillations. We also receive
the neutrino transition probability when a particle propagates in the
gravitational field of a rotating massive object. Then we apply the general
technique to the description of neutrino spin oscillations in the Schwarzschild
metric. The neutrino spin evolution equation for the case of the neutrino
motion in the vicinity of a black hole is obtained. The effective Hamiltonian
and the transition probability are also derived. We examine the neutrino
oscillations process on different circular orbits and analyze the frequencies
of spin transitions. The validity of the quasi-classical approach is also
considered.
