  We explore integrability properties of superstring equations of motion in
AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges
and construct a Lax representation for the corresponding Hamiltonian dynamics
on subspace of physical superstring degrees of freedom. We present some
explicit results for the corresponding conserved charges by consistently
reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both
bosonic and fermionic fields.
