We study supersymmetric harmonic maps from the point of view of integrable
system. It is well known that harmonic maps from R^2 into a symmetric space are
solutions of a integrable system . We show here that the superharmonic maps
from R^{2|2} into a symmetric space are solutions of a integrable system, more
precisely of a first elliptic integrable system in the sense of C.L. Terng and
that we have a Weierstrass-type representation in terms of holomorphic
potentials (as well as of meromorphic potentials). In the end of the paper we
show that superprimitive maps from R^{2|2} into a 4-symmetric space give us, by
restriction to R^2, solutions of the second elliptic system associated to the
previous 4-symmetric space.