The sensitivity to a light Higgs boson in the general 2HDM (II), with a mass below 40 GeV, is estimated for an future ee 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 → bb̄h(A),→ τ τ̄h(A), and the decay Z→h(A) + γ. Although the discovery potential is c...