  We have proposed the non-Abelian dual superconductivity picture for quark
confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical
evidences for the restricted-field dominance and the non-Abelian magnetic
monopole dominance in the string tension by applying a new formulation of the
YM theory on a lattice. To establish the non-Abelian dual superconductivity
picture for quark confinement, we have observed the non-Abelian dual Meissner
effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux
created by the quark-antiquark source, and the non-Abelian magnetic monopole
currents induced around the flux. We conclude that the dual superconductivity
of the SU(3) Yang-Mills theory is strictly the type I and that this type of
dual superconductivity is reproduced by the restricted field and the
non-Abelian magnetic monopole part, in sharp contrast to the SU(2) case: the
border of type I and type II.
