  The phase separation and vortex states in two-component Bose-Einstein
condensate consisting of $|F=1,m_f=-1>$ and $|2,1>$ internal spin states of
$^{87}Rb$ atoms are considered in the framework of Thomas-Fermi approximation.
It is shown that in nonrotating system the atoms in the state $|1,-1>$ form a
shell about the atoms in the state $|2,1>$. The critical angular velocity for
each state is calculated. These velocities are drastically dependent on the
mutual concentrations of the components, the critical angular velocity of the
outer component being less than the angular velocity of the inner one. It is
shown that the atoms in the $|1,-1>$ state can form a rotating ring about the
resting core of the atoms in the state $|2,1>$.
