  Given a irreducible automorphic representation $\Pi$ of a similitude group
$G/\mathbb Q$ giving rise to a KHT-Shimura variety, given a local congruence of
the local component of $\Pi$ at a fixed place $p$, we justify the existence of
a global automorphic representation $\Pi'$ with the same weight and the same
level outside $p$ than $\Pi$, such that $\Pi$ and $\Pi'$ are weakly congruent.
The arguments rest on the separation of the various contributions coming either
from torsion or on the distinct families of automorphic representations, to the
modulo $l$ reduction of the cohomology of Harris-Taylor perverse sheaves.
