  We present a superconformally invariant and integrable model based on the
twisted affine Kac-Moody superalgebra $\hat{osp(2|2)}^{(2)}$ which is the
supersymmetrization of the purely bosonic conformal affine Liouville theory
recently proposed by Babelon and Bonora. Our model reduces to the
super-Liouville or to the super sinh-Gordon theories under certain limit
conditions and can be obtained, via hamiltonian reduction, from a superspace
WZNW model with values in the corresponding affine KM supergroup. The
reconstruction formulae for classical solutions are given. The classical
$r$-matrices in the homogeneous grading and the exchange algebras are worked
out.
