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Pour tout $t\in\mN$ nous d\'efinissons un certain entier positif $\N_t$ etnous conjecturons: si $H$ est un fibr\'e de Gauss-Manin d'une fibrationsemi-stable alors la $t$-\`eme classe de Chern de $H$ est annul\'ee par $\N_t$.Nous d\'emontrons diverses cons\'equences de cette conjecture.  For any $t\in\mN$, we define a certain positive integer $\N_t$ and weconjecture: if $H$ is a Gauss-Manin bundle of a semi-stable fibration then the$t$-th Chern class of $H$ is kiled by $\N_t$. We prove various consequences ofthis conjecture.

Une conjecture sur la torsion des classes de Chern des fibr\'es de Gauss-Manin