Non-standard supersymmetries on spaces admitting Killing-Yano tensors

We attempt to point out the intimate relation between Killing-Yano tensors and non-standard supersymmetries, along the way reviewing some recent results. The Euclidean Taub-NUT space is taken to illustrate some of the aspects of the general discussion about the connection between spacetime higher order geometrical symmetries and supersymmetries. The dynamical symmetry of this space leads in a natural way to an infinite dimensional twisted loop superalgebra of the conserved operators.