We describe the universal linearized action for massless superfields o
f all superspins in N = 1, D = 4 anti-de Sitter superspace as a gauge
theory of unconstrained superfields taking their values in the commuta
tive algebra of analytic functions over a one-sheeted hyperboloid in R
(3,1). The action is invariant under N = 2 supersymmetry transformatio
ns which form a closed algebra off the mass-shell.