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 behaviour 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.