Supplementation of reducible constraints and the Green-Schwarz superstring

We apply the supplementation trick Phys. Lett. B 381 (1996) 105 to the Gree n-Schwarz superstring. For type IIB theory both first and second class cons traints are covariantly separated and then arranged into irreducible sets i n the initial formulation. For N = 1 Green-Schwarz superstring we propose a modified action which is equivalent to the initial one. Fermionic first an d second class constraints are covariantly separated, the first class const raints (ICC) turn out to be irreducible. We discuss also equations of motio n in the covariant gauge for kappa -symmetry. For type IIA theory the same modification leads to formulation with irreducible second class constraints . (C) 2001 Published by Elsevier Science B.V.