  We construct unitary representations of (1,0) and (2,0) superconformal
algebras in six dimensions by using superfields defined on harmonic superspaces
with coset manifolds USp(2n)/[U(1)]^n, n=1,2. In the spirit of the AdS_7/CFT_6
correspondence massless conformal fields correspond to "supersingletons" in
AdS_7. By tensoring them we produce all short representations corresponding to
1/2 and 1/4 BPS anti-de Sitter bulk states of which "massless bulk"
representations are particular cases.
