  We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter
supergravity and study its asymptotic symmetries. The theory is described by
the Chern-Simons action based on a real, infinite-dimensional higher-spin
superalgebra. We specify consistent boundary conditions on the higher-spin
super-gauge connection corresponding to asymptotically anti-de Sitter
spacetimes. We then determine the residual gauge transformations that preserve
these asymptotic conditions and compute their Poisson bracket algebra. We find
that the asymptotic symmetry is enhanced from the higher-spin superalgebra to
some (N,M)-extended super-W(infinity) nonlinear superalgebra. The latter has
the same classical central charge as pure Einstein gravity. Special attention
is paid to the (1,1)-case. Truncation to the bosonic sector yields the
previously found W(infinity) algebra, while truncation to the underlying
finite-dimensional superalgebra reproduces the N-extended superconformal
algebra (in its nonlinear version for N>2). We discuss string theory
realization of these higher-spin anti-de Sitter supergravity theories as well
as relations to previous treatments of super-W(infinity) in the literature.
