  In this article, we consider the links between parabolic induction and the
local Langlands correspondence. We enunciate a conjecture about the (enhanced)
Langlands parameters of supercuspidal representation of split reductives
$p$-adics groups. We are able to verify this in those known cases of the local
Langlands correspondence for linear groups and classical groups. Furthermore,
in the case of classical groups, we can construct the "cuspidal support" of an
enhanced Langlands parameter and get a decomposition of the set of enhanced
Langlands parameters a la Bernstein. We check that these constructions match
under the Langlands correspondence and as consequence, we obtain the
compatibility of the Langlands correspondence with parabolic induction.
