The sensitivity to a light Higgs boson in the general 2HDM (II), with a mass below 40 GeV, is estimated for a future e~+e~- Linear Collider operating with a very high luminosity at the Z peak (GigaZ). We consider possible Higgs boson production via the Bjorken process, the (hA) pair production, the Yukawa process Z → bb-barh(A), → ττ-barh(A), and the decay Z τ h(A) + γ. Although the discovery potential is considerably extended compared to the current sensitivities, mainly from LEP, the existence of a h or A even with a mass of a few GeV cannot be excluded with two billion Z decays. The need to study the very light Higgs scenario at a e~+e~- Linear Collider running at several hundred GeV and the LHC is emphasized.
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