  We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent
gauge fields. We prove that the non-Abelian AB phase shift related to
time-dependent gauge fields, in which the electric and magnetic fields are
written in the adjoint representation of $SU(N)$ generators, vanishes up to the
first order expansion of the phase factor. Therefore, the flux quantization in
a superconductor ring does not appear in the time-dependent Abelian or
non-Abelian AB effect.
