  In this paper we study the spectrum of all conformal, ${\cal N}$-extended
supergravities (${\cal N}=1,2,3,4$) in four space-time dimensions. When these
theories are obtained as massless limit of Einstein plus Weyl$^2$supergravity,
the appropriate counting of the enhanced gauge symmetries allow us to derive
the massless spectrum which consist of a dipole ghost graviton multiplet, a
${\cal N}$-fold tripole ghost gravitino, the third state belonging to a spin
3/2 multiplet and a residual vector multiplet present for non-maximal ${\cal
N}<4$ theories. These theories are not expected to have a standard gravity
holographic dual in five dimensions.
