  Local higher-spin conserved currents are constructed in the supersymmetric
sigma models with target manifolds symmetric spaces $G/H$. One class of
currents is based on generators of the de Rham cohomology ring of $G/H$; a
second class of currents are higher-spin generalizations of the
(super)energy-momentum tensor. A comprehensive analysis of the invariant
tensors required to construct these currents is given from two complimentary
points of view, and sets of primitive currents are identified from which all
others can be constructed as differential polynomials. The Poisson bracket
algebra of the top component charges of the primitive currents is calculated.
It is shown that one can choose the primitive currents so that the bosonic
charges all Poisson-commute, while the fermionic charges obey an algebra which
is a form of higher-spin generalization of supersymmetry. Brief comments are
made on some implications for the quantized theories.
