  Let $\Fl_\lambda$ be a generalized flag variety of a simple Lie group $G$
embedded into the projectivization of an irreducible $G$-module $V_\lambda$. We
define a flat degeneration $\Fl_\lambda^a$, which is a ${\mathbb G}^M_a$
variety. Moreover, there exists a larger group $G^a$ acting on $\Fl_\lambda^a$,
which is a degeneration of the group $G$. The group $G^a$ contains ${\mathbb
G}^M_a$ as a normal subgroup. If $G$ is of type $A$, then the degenerate flag
varieties can be embedded into the product of Grassmanians and thus to the
product of projective spaces. The defining ideal of $\Fl^a_\lambda$ is
generated by the set of degenerate Pl\" ucker relations. We prove that the
coordinate ring of $\Fl_\lambda^a$ is isomorphic to a direct sum of dual
PBW-graded $\g$-modules. We also prove that there exist bases in
multi-homogeneous components of the coordinate rings, parametrized by the
semistandard PBW-tableux, which are analogues of semistandard tableux.
