  We demonstrate how actions for interacting superconformal field theories in
(p+1)-dimensions arise as a result of gauge fixing worldvolume diffeomorphisms
and fermionic kappa-symmetry in actions for super-p-branes propagating in
superbackgrounds of AdS(p+2)xS(D-p-2) geometry. The method of nonlinear
realizations and coset spaces is used for getting an explicit form of
supervielbeins and superconnections of the AdSxS superbackgrounds, which are
required for the construction of the superconformal theories. Subtleties of
consistent gauge fixing worldvolume symmetries of the branes are discussed.
