  We consider neutrino mixing and oscillations in presence of an arbitrary
constant magnetic field with nonzero transversal $B_{\perp}$ and longitudinal
$B_{\parallel}$ components with respect to the direction of neutrino
propagation. The electromagnetic interaction of neutrinos is determined by
diagonal and transition neutrino magnetic moments that are introduced for the
neutrino mass states. Explicit expressions for the effective neutrino diagonal
and transition magnetic moments for the flavor basis in terms of these values
for the mass states are obtained. The effective evolution Hamiltonian for the
flavor neutrino and the corresponding oscillation probability are derived. The
role of the longitudinal magnetic field component is examined. In particular,
it is shown that: 1) $B_{\parallel}$ coupled to the corresponding magnetic
moments shifts the neutrino energy, and 2) in case of nonvanishing neutrino
transition magnetic moments $B_{\parallel}$ produces an additional mixing
between neutrino states, both in the mass and flavor neutrino bases.
