In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $sl_2^1oplus sl_2^2oplus dots oplus sl_2^soplus R,$ where $R$ is a solvable radical. The classifications of such Leibniz algebras in t
he cases $dim R=2, 3$ and $dim I eq 3$ have been obtained. Moreover, we classify Leibniz algebras with $L/Icong sl_2^1oplus sl_2^2$ and some conditions on ideal $I=id<[x,x] | xin L>.$
We present the classification of a subclass of $n$-dimensional naturally graded Zinbiel algebras. This subclass has the nilindex $n-3$ and the characteristic sequence $(n-3,2,1).$ In fact, this result completes the classification of naturally graded Zinbiel algebras of nilindex $n-3.$
