  The manner in which the parameters of a two-Higgs-doublet model can be chosen
so that no Higgs boson is discovered at a $\sqrt{s}\leq 800\gev$ $\epem$
collider, while maintaining consistency with current precision electroweak
measurements, is described. The importance of a Giga-$Z$ factory and higher
collider energies for such a scenario is emphasized.
