  We present the first computations of quasiequilibrium binary neutron stars
with different mass components in general relativity, within the
Isenberg-Wilson-Mathews approximation. We consider both cases of synchronized
rotation and irrotational motion. A polytropic equation of state is used with
the adiabatic index gamma=2. The computations have been performed for the
following combinations of stars: (M/R)_{star 1} vs. (M/R)_{star 2} = 0.12 vs.
(0.12, 0.13, 0.14), 0.14 vs. (0.14, 0.15, 0.16), 0.16 vs. (0.16, 0.17, 0.18),
and 0.18 vs. 0.18, where (M/R) denotes the compactness parameter of infinitely
separated stars of the same baryon number. It is found that for identical mass
binary systems there is no turning point of the binding energy (ADM mass)
before the end point of the sequence (mass shedding point) in the irrotational
case, while there is one before the end point of the sequence (contact point)
in the synchronized case. On the other hand, in the different mass case, the
sequence ends by the tidal disruption of the less massive star (mass shedding
point). It is then more difficult to find a turning point in the ADM mass.
Furthermore, we find that the deformation of each star depends mainly on the
orbital separation and the mass ratio and very weakly on its compactness. On
the other side, the decrease of the central energy density depends on the
compactness of the star and not on that of the companion.
