  We present electric-magnetic (Hodge) duality formulation for non-Abelian
gauge groups with N=1 supersymmetry in 3+1 (4D) dimensions. Our system consists
of three multiplets: (i) A super-Yang-Mills vector multiplet (YMVM)
$(A_\mu{}^I, \lambda^I)$, (ii) a dual vector multiplet (DVM) $(B_\mu{}^I,
\chi^I)$, and (iii) an unphysical tensor multiplet (TM) $(C_{\mu\nu}{}^I,
\rho^I, \varphi^I)$, with the index I for adjoint representation. The
multiplets YMVM and DVM are dual to each other like: $G_{\mu\nu}{}^I = (1/2)
\epsilon_{\mu\nu}{}^{\rho\sigma} F_{\rho\sigma}{}^I$. The TM is unphysical, but
still plays an important role for establishing the total consistency of the
system, based on recently-developed tensor-hierarchy formulation. We also apply
this technique to non-Abelian electric-magnetic duality in 9+1 (10D)
dimensions. The extra bosonic auxiliary field $K_{\mu_1\cdots\mu_6}$ in 10D is
shown to play an important role for the closure of supersymmetry on fields.
