  We investigate the spin $1/2$ fermions on quantum two spheres. It is shown
that the wave functions of fermions and a Dirac Operator on quantum two spheres
can be constructed in a manifestly covariant way under the quantum group
$SU(2)_q$. The concept of total angular momentum and chirality can be expressed
by using $q$-analog of Pauli-matrices and appropriate commutation relations.
