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