  Locally supersymmetric systems in odd dimensions whose Lagrangians are
Chern-Simons forms for supersymmetric extensions of anti-de Sitter gravity are
discussed. The construction is illustrated for D=7 and 11. In seven dimensions
the theory is an N=2 supergravity whose fields are the vielbein
($e_{\mu}^{a}$), the spin connection ($\omega_{\mu}^{ab}$), two gravitini
($\psi_{\mu}^{i}$) and an $sp(2)$ gauge connection ($a_{\mu j}^{i}$). These
fields form a connection for $osp(2|8)$. In eleven dimensions the theory is an
N=1 supergravity containing, apart from $e_{\mu}^{a}$ and $\omega_{\mu}^{ab}$,
one gravitino $\psi_{\mu}$, and a totally antisymmetric fifth rank Lorentz
tensor one-form, $b_{\mu}^{abcde}$. These fields form a connection for
$osp(32|1)$. The actions are by construction invariant under local
supersymmetry and the algebra closes off shell without requiring auxiliary
fields. The $N=2^{[D/2]}$-theory can be shown to have nonnegative energy around
an AdS background, which is a classical solution that saturates the Bogomolnyi
bound obtained from the superalgebra.
