Torsions of connections on higher order cotangent bundles

By a torsion of a general connection Gamma on a fibered manifold Y --> M we understand the Frolicher-Nijenhuis bracket of Gamma and some canonical tangent valued oneform (affinor) on Y. Using all natural affinors on higher order cotangent bundles, we determine all torsions of general connections on such bundles. We present the geometrical interpretation and study some properties of the torsions.