The sensitivity to a light Higgs boson in the general 2HDM (II), with a mass below 40 GeV, is estimated for an future e + e − linear collider operating with very high luminosity at the Z peak (GigaZ). We consider a possible Higgs boson production via the Bjorken process, the (hA) pair production, the Yukawa process Z → bbh(A), → ττ h(A), and the decay Z→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 linear e + e − collider running at several hundred GeV and the LHC is emphasised.