In 1990, J.L. Krivine introduced the notion of storage operator to simulate, for Church integers, the ``call by value'' in a context of a ``call by name'' strategy. In this present paper, we define, for every $\lambda$-term S which realizes the successor function on Church integers, the notion of S-storage operator. We prove that every storage operator is a $S-storage operator. But the converse is not always true.