  Using the off-shell formulation for ${\cal N}=2$ conformal supergravity in
four dimensions, we describe superconformal higher-spin multiplets of conserved
currents in a curved background and present their associated unconstrained
gauge prepotentials. The latter are used to construct locally superconformal
chiral actions, which are demonstrated to be gauge invariant in arbitrary
conformally flat backgrounds. The main ${\cal N}=2$ results are then
generalised to the ${\cal N}$-extended case. We also present the
gauge-invariant field strengths for on-shell massless higher-spin ${\cal N}=2$
supermultiplets in anti-de Sitter space. These field strengths prove to furnish
representations of the ${\cal N}=2$ superconformal group.
