  We find a minimal differential graded (dg) operad whose generic
representations in $R^n$ are in one-to-one correspondence with formal germs of
those endomorphisms of the tangent bundle to $R^n$ which satisfy the Nijenhuis
integrability condition. This operad is of a surprisingly simple origin -- it
is the cobar construction on the quadratic operad of homologically trivial dg
Lie algebras. As a by product we obtain a strong homotopy generalization of
this geometric structure and show its homotopy equivalence to the structure of
contractible dg manifold.
