  Fock module realization for the unitary singleton representations of the
$d-1$ dimensional conformal algebra $o(d-1,2)$, which correspond to the spaces
of one-particle states of massless scalar and spinor in $d-1$ dimensions, is
given. The pattern of the tensor product of a pair of singletons is analyzed in
any dimension. It is shown that for $d>3$ the tensor product of two boson
singletons decomposes into a sum of all integer spin totally symmetric massless
representations in $AdS_d$, the tensor product of boson and fermion singletons
gives a sum of all half-integer spin symmetric massless representations in
$AdS_d$, and the tensor product of two fermion singletons in $d>4$ gives rise
to massless fields of mixed symmetry types in $AdS_d$ depicted by Young
tableaux with one row and one column together with certain totally
antisymmetric massive fields. In the special case of $o(2,2)$, tensor products
of 2d massless scalar and/or spinor modules contain infinite sets of 2d
massless conformal fields of different spins. The obtained results extend the
4d result of Flato and Fronsdal \cite{FF} to any dimension and provide a
nontrivial consistency check for the recently proposed higher spin model in
$AdS_d$ \cite{d}. We define a class of higher spin superalgebras which act on
the supersingleton and higher spin states in any dimension. For the cases of
$AdS_3$, $AdS_4$, and $AdS_5$ the isomorphisms with the higher spin
superalgebras defined earlier in terms of spinor generating elements are
established.
