  We describe new non-supersymmetric conformal field theories in three and four
dimensions, using the CFT/AdS correspondence. In order to believe in their
existence at large N_c and strong 't Hooft coupling, we explicitly check the
stability of the corresponding non-supersymmetric anti-de Sitter backgrounds.
Cases of particular interest are the relevant deformations of the N=4 SCFT in
SU(3) and SO(5) invariant directions. It turns out that the former is a stable,
and the latter an unstable non-supersymmetric type IIB background.
