  We show that the stress-energy tensor for a superstring in the AdS5xS5
background is written in a supersymmetric generalized "Sugawara" form. It is
the "supertrace" of the square of the right-invariant current which is the
Noether current satisfying the flatness condition. The Wess-Zumino term is
taken into account through the supersymmetric gauge connection in the
right-invariant currents, therefore the obtained stress-energy tensor is kappa
invariant. The integrability of the AdS superstring provides an infinite number
of the conserved "local" currents which are supertraces of the n-th power of
the right-invariant current. For even n the "local" current reduces to terms
proportional to the Virasoro constraint and the kappa symmetry constraint,
while for odd n it reduces to a term proportional to the kappa symmetry
constraint .
