  In this paper we identify the structure of complex finite-dimensional Leibniz
algebras with associated Lie algebras $sl_2^1\oplus sl_2^2\oplus \dots \oplus
sl_2^s\oplus R,$ where $R$ is a solvable radical. The classifications of such
Leibniz algebras in the cases $dim R=2, 3$ and $dim I\neq 3$ have been
obtained. Moreover, we classify Leibniz algebras with $L/I\cong sl_2^1\oplus
sl_2^2$ and some conditions on ideal $I=id<[x,x] \ | \ x\in L>.$
