The conserved supercurrents J(++) and J(--) are deduced for the (4, 0) supe
rsymmetric sigma-model on harmonic superspace with arbitrary background gau
ge connection. These are introduced in the Lagrangian density of the model
by their couplings to the analytic gauge superfields Gamma(--) and Gamma(+). The T-duality transformations are obtained by integrating out the analyt
ic gauge superfields. Finally, the (4, 0) supersymmetric anomaly is derived
.