We construct a one-parameter family of flat currents in AdS 5 ×S 1 and AdS 3 ×S 3 Green-Schwarz superstrings, which would naturally lead to a hierarchy of classical conserved nonlocal charges. In the former case we rewrite the AdS 5 × S 1 string using a new Z 4graded base of the superalgebra su(2, 2|2). In both cases the existence of the Z 4 grading in the superalgebras plays a key role in the construction. As a result, we find that the flat currents, when formally written in terms of the G 0 -gauge invariant lowercase 1-forms, take the same form as the one in AdS 5 × S 5 case. *