We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The correct account for the spin influence on the particle trajectory is obtained with the noncovariant description of spin. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is demonstrated that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals to unity (as well as for the charged Kerr hole the gyromagnetic ratio equals to two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.