  The classical exchange algebra satisfied by the monodromy matrix of AdS5 x S5
string theory in the Green-Schwarz formulation is determined by using a
first-order Hamiltonian formulation and by adding to the Bena-Polchinski-Roiban
Lax connection terms proportional to constraints. This enables in particular to
show that the conserved charges of this theory are in involution. This result
is obtained for a general world-sheet metric. The same exchange algebra is
obtained within the pure spinor description of AdS5 x S5 string theory. These
results are compared to the one obtained by A. Mikhailov and S. Schaefer-Nameki
for the pure spinor formulation.
