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A numeral system is a sequence of an infinite different closed normal$\lambda$-terms which has closed $\lambda$-terms for successor and zero test. Anumeral system is said adequate iff it has a closed $\lambda$-term forpredecessor. A storage operator for a numeral system is a closed $\lambda$-termwhich simulate "call-by-value" in the context of a "call-by-name" strategy. E.Tronci conjectured the following result : a numeral system is adequate if ithas a storage operator. This paper gives a negative answer to this conjecturefor the numeral systems typable in the J.-Y. Girard type system F. The E.Tronci's conjecture remains open in pure $\lambda$-calculus.

Une r\'eponse n\'egative \`a la conjecture de E. Tronci pour les syst\`emes num\'eriques typ\'es