  Modelling as a dipole the magnetic interaction of a binary system of neutron
stars, we are able to include the magnetic effects in the Newtonian and in the
inspiral dynamics of the system using an equivalent one-body description.
Furthermore, in the inspiral stage we determine the role of the magnetic
interaction in the waveforms generated by the system and obtain explicit
formulas for the decrease in the separation of the stars, the time to reach a
minimal radius, the gravitational luminosity and the change of gravitational
wave frequency, all this within the quadrupole approximation. For the magnitude
of the magnetic field that is consider to exist in these binaries $\sim 10^{16}
{\rm G}$ we are able to show that its effect on the observable quantities is of
the order of the 2PN correction, already close to the detection range of the
gravitational waves observatories. %} We also discuss cases in which the
magnetic field could have a more significant influence.
