  We investigate systematically the asymptotic dynamics and symmetries of all
three-dimensional extended AdS supergravity models. First, starting from the
Chern-Simons formulation, we show explicitly that the (super)anti-de Sitter
boundary conditions imply that the asymptotic symmetry algebra is the extended
superconformal algebra with quadratic nonlinearies in the currents. We then
derive the super-Liouville action by solving the Chern-Simons theory and obtain
a realization of the superconformal algebras in terms of super-Liouville
fields. Finally, we discuss the possible periodic conditions that can be
imposed on the generators of the algebra and generalize the spectral flow
analysed previously in the context of the $N$-extended linear superconformal
algebras with $N \leq 4$. The $(2+1)$-AdS/2-CFT correspondence sheds a new
light on the properties of the nonlinear superconformal algebras. It also
provides a general and natural interpretation of the spectral flow.
