  Free massless higher-superspin superfields on the N=1, D=4 anti-de Sitter
superspace are introduced. The linearized gauge transformations are postulated.
Two families of dually equivalent gauge-invariant action functionals are
constructed for massless half-integer-superspin s+1/2 (s >= 2) and
integer-superspin s (s >= 1) superfields. For s=1, one of the formulations for
half-integer superspin multiplets reduces to linearized minimal N=1
supergravity with a cosmological term, while the other is the lifting to the
anti-de Sitter superspace of linearized non-minimal n=-1 supergravity.
