  Quasi-Lie bialgebras are natural extensions of Lie-bialgebras, where the
cobracket satisfies the co-Jacobi relation up to some natural obstruction
controlled by a skew-symmetric 3-tensor $\phi$. This structure was introduced
by Drinfeld while studying deformation theory of universal enveloping algebras
and has since seen many other applications in algebra and geometry. In this
paper we study the derivation complex of strongly homotopy quasi-Lie bialgebra,
both in the unwheeled (i.e standard) and wheeled case, and compute its
cohomology in terms of Kontsevich graph complexes.
