As a step towards formulating projective superspace techniques for supergravity theories with eight supercharges, this work is devoted to field theory in live-dimensional M = I anti-de Sitter superspace AdS(5 vertical bar 8) = SU(2, 2 vertical bar 1)/SO(4, 1) x U(1) which is a maximally symmetric curved background. We develop the differential geometry of AdS(5 vertical bar 8) and describe its isometries in terms of Killing supervectors. Various off-shell supermultiplets in AdS(5 vertical bar 8) x S-2 are defined, and supersymmetric actions are constructed both in harmonic and projective superspace approaches. Several families of supersymmetric theories are presented including nonlinear sigma-models, Chern-Simons theories and vector-tensor dynamical systems. Using a suitable coset representative, we make use of the coset construction to develop ail explicit realization for one half of the superspace AdS518 as a trivial fiber bundle with fibers isomorphic to four-dimensional Minkowski superspace. (C) 2007 Elsevier B.V. All rights reserved.