We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the Script N-extented self-dual super Yang-Mills equations for general Script N⩽ 4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the Script N-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn—by a supersymmetric extension of Ward's conjecture—reduce to the super hierarchies of integrable models in D< 4 dimensions.