  The motion of spinning relativistic particles in external electromagnetic and
gravitational fields is considered. Covariant equations for this motion are
demonstrated to possess pathological solutions, when treated nonperturbatively
in spin. A self-consistent approach to the problem is formulated, based on the
noncovariant description of spin and on the usual, ``naive'' definition of the
coordinate of a relativistic particle. A simple description of the
gravitational interaction of first order in spin, is pointed out for a
relativistic particle. The approach developed allows one to consider effects of
higher order in spin. Explicit expression for the second-order Hamiltonian is
presented. We discuss the gravimagnetic moment, which is a special spin effect
in general relativity.
