  We determine the representations of the ``conformal'' group ${\bar{SO}}_0(2,
n)$, the restriction of which on the ``Poincar\'e'' subgroup ${\bar{SO}}_0(1,
n-1).T_n$ are unitary irreducible. We study their restrictions to the ``De
Sitter'' subgroups ${\bar{SO}}_0(1, n)$ and ${\bar{SO}}_0(2, n-1)$ (they remain
irreducible or decompose into a sum of two) and the contraction of the latter
to ``Poincar\'e''. Then we discuss the notion of masslessness in $n$ dimensions
and compare the situation for general $n$ with the well-known case of
4-dimensional space-time, showing the specificity of the latter.
