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Let M and N be differential manifolds and J and L be foliations on M and N respectively. In this work we define the (J,L) - stability and the infinitesimal (J,L) - stability for mappings f : M → N . We give some caracterizations of the infinitesimal (J,L) - stability, and we prove the following theorem: "If M is compact, f takes leaves of J into leaves of L and f is infinitesimal (J,L) - stable, then f is (J,L) - stable".