  Spin precession equations including the spin-orbit (SO), spin-spin (SS),
quadrupole-monopole (QM) and magnetic dipole-magnetic dipole (DD) leading-order
interactions are derived for compact binary systems in order to investigate the
DD contribution in the orbit-averaged spin precession equations for binary
neutron star systems neglecting the gravitational radiation-reaction effect. It
is known that the magnitudes of spins are not conserved quantities due to the
DD interaction. We give a simple analytical description for the pure DD
interaction making the magnitudes of spins almost constant by neglecting the
SO, SS and QM contributions. We also demonstrate the evolutions of the relative
angles of spins and magnetic dipoles with the help of numeric simulations
including all contributions (SO, SS, QM and DD) and introduce a dimensionless
magnetic dipole parameter to characterize the strength of magnetic fields for
some realistic neutron star binaries. We find that for realistic configurations
the strong magnetic fields of neutron stars can modify the spin dynamics over
long periods of time.

General Relativity and Quantum Cosmology