  We introduce a new type of algebra, which is called a Lie-Leibniz algebra.
This concept is an abstraction of derived bracket construction. It will be
proved that the operad of Lie-Leibniz algebras is Koszul. The strong homotopy
version of derived bracket Leibniz algebras will be discussed. We will get some
new results with respect to sh Lie and sh Leibniz algebras.
