  In this paper we study the charge and spin currents transported by the
elementary excitations of the one-dimensional Hubbard model. The corresponding
current spectra are obtained by both analytic methods and numerical solution of
the Bethe-ansatz equations. For the case of half-filling, we find that the
spin-triplet excitations carry spin but no charge, while charge $\eta$-spin
triplet excitations carry charge but no spin, and both spin-singlet and charge
$\eta$-spin-singlet excitations carry neither spin nor charge currents.
