A model for binary evolution is introduced which can determine whether the
rotation of components is synchronized with the orbital motion, and can cal
culate the evolution of both the synchronized and non-synchronized binary s
ystems. With this model, the evolution of a binary system consisting of a 9
M. star and a 6 M. star is studied with mass transfer Case B. The result s
hows that the synchronization of the rotational and orbital periods can be
reached when the binary system is a detached system and before the occurren
ce of the first mass transfer. After the onset of the first mass transfer,
the binary system becomes non-synchronized. The mass accepted component (th
e secondary) rotates faster with a period much smaller than that of the orb
ital motion.