EN
We study the problem of how a map f:M → ℝ on an n-manifold M induces canonically an affinor $A(f): TT^{(r)}M → TT^{(r)}M$ on the vector r-tangent bundle $T^{(r)}M = (J^r(M,ℝ)₀)*$ over M. This problem is reflected in the concept of natural operators $A:T^{(0,0)}_{|ℳ fₙ} ⇝ T^{(1,1)}T^{(r)}$. For integers r ≥ 1 and n ≥ 2 we prove that the space of all such operators is a free (r+1)²-dimensional module over $𝓒^{∞}(T^{(r)}ℝ)$ and we construct explicitly a basis of this module.