Flat currents, Zm gradings and coset space actions

The construction of flat currents, and hence conserved non-local charges, for the superstring on AdS5×S5 is generalised. It is shown that such currents exist for sigma-model type actions on all coset (super-)spaces G/H in which, at the level of the Lie algebras, h is the grade-zero subspace of a Zm-grading of g. This is true for an essentially unique choice of the Wess-Zumino term, which is determined.