  In general neutron stars in binaries are spinning. Due to the existence of
millisecond pulsars we know that these spins can be substantial. We argue that
spins with periods on the order a few dozen milliseconds could influence the
late inspiral and merger dynamics. Thus numerical simulations of the last few
orbits and the merger should start from initial conditions that allow for
arbitrary spins. We discuss quasi-equilibrium approximations one can make in
the construction of binary neutron star initial data with spins. Using these
approximations we are able to derive two new matter equations. As in the case
of irrotational neutron star binaries one of these equations is algebraic and
the other elliptic. If these new matter equations are solved together with the
equations for the metric variables following the Wilson-Mathews or conformal
thin sandwich approach one can construct neutron star initial data. The spin of
each star is described by a rotational velocity that can be chosen freely so
that one can create stars in arbitrary rotation states. Our new matter
equations reduce to the well known limits of both corotating and irrotational
neutron star binaries.
