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This article deals with a Leibniz superalgebra L = L 0 ⊕ L 1 , whose even part is a simple Lie algebra sl 2 . We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on sl 2 . We show that there exist such Leibniz superalgebra with nontrivial odd part only in case of dimL 1 = 2.

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In this paper solvable Leibniz algebras whose nilradical is quasi-filiform Lie algebra of maximum length, are classified. The rigidity of such Leibniz algebras with two-dimensional complemented space to nilradical is proved.