  The new extensions of the Poincar\'e superalgebra recently found in ten and
eleven dimensions are shown to admit a linear realization. The generators of
the nonlinear and linear group transformations are shown to fall into
equivalent representations of the superalgebra. The parametrization of the
coset space $G/H$, with $G$ a given extended supergroup and $H$ the Lorentz
subgroup, that corresponds to the linear transformations is presented.
