  The superconformal structure of coset superspaces with AdS_m x S^n geometry
of bosonic subspaces is studied. It is shown, in particular, that the
conventional superspace extensions of the coset manifolds AdS_2 x S^2, AdS_3 x
S^3 and AdS_5 x S^5, which arise as solutions of corresponding D=4,6, 10
supergravities and have been extensively studied in connection with AdS/CFT
correspondence, are not superconformally flat, though their bosonic
submanifolds are conformally flat. We give a group-theoretical reasoning for
this fact. We find that in the AdS_2 x S^2 and AdS_3 x S^3 cases there exist
different supercosets based on the supergroup OSp(4^*|2) which are
superconformally flat. We also argue that in D=2,3,4 and 5 there exist
superconformally flat `pure' AdS_D supercosets. Two methods of checking the
superconformal flatness are proposed. One of them consists in solving the
Maurer-Cartan structure equations and the other is based on embedding the
isometry supergroup of the AdS_m x S^n superspace into a superconformal group
in (m+n)-dimensional Minkowski space. Finally, we discuss some applications of
the above results to the description of supersymmetric dynamical systems.
