  We describe conformal operators living at the boundary of $AdS_{d+1}$ in a
general setting. Primary conformal operators at the threshold of the unitarity
bounds of UIR's of O(d,2) correspond to singletons and massless fields in
$AdS_{d+1}$, respectively. For maximal supersymmetric theories in $AdS_{d+1}$
we describe ``chiral'' primary short supermultiplets and non-chiral primary
long supermultiplets. Examples are exhibited which correspond to KK and string
states. We give the general contribution of a primary conformal operator to the
OPE and Green's functions of primary fields, which may be relevant to compute
string corrections to the four-point supergraviton amplitude in Anti-de-Sitter
space. The material in this paper was presented by one of the authors (S.F) at
String 98, Santa Barbara.
