  The presence of Killing-Yano tensors implies the existence of non-standard
supersymmetries in point particle theories on curved backgrounds. In a string
theoretical context these are symmetries of the modes describing the
particle-like behavior of the string. In the presence of isometries we show
that, in addition to these, one can also define a new type of non-standard
supersymmetry among a mixture of particle and winding modes. The interplay with
T-duality is also examined and illustrated by explicit examples.
