  The notions of Zinbiel 2-algebras and 2-term $Z_{\infty}$-algebras are
introduced and studied. It is proved that the category of Zinbiel 2-algebras
and the category of $2$-term $Z_{\infty}$-algebras are equivalent. Relationship
between Zinbiel 2-algebras and dendriform 2-algebras are found.
