  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.
