  Recently S. Merkulov established a new link between differential geometry and
homological algebra by giving descriptions of several differential geometric
structures in terms of algebraic operads and props. In particular he described
Nijenhuis structures as corresponding to representations of the cobar
construction on the Koszul dual of a certain quadratic operad. In this paper we
prove, using the PBW-basis method of E. Hoffbeck, that the operad governing
Nijenhuis structures is Koszul, thereby showing that Nijenhuis structures
correspond to representations of the minimal resolution of this operad. We also
construct an operad such that representations of its minimal resolution in a
vector space V are in one-to-one correspondence with pairs of compatible
Nijenhuis structures on the formal manifold associated to V.
