  In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact algebra
$G_{2(2)}$ which is split real form of $G_2$. We give the classification of
reducible Verma modules $G_2$. We give also the singular vectors between these
modules, thus setting the stage for construction of the invariant differential
operators over $G_{2(2)}$.
