  Assuming perturbativity up to a high energy scale $\sim 10^{16}$ GeV, we
demonstrate that a future $e^+e^-$ linear collider operating at $\sqrt{s} =$
500 GeV with $\int{\cal L}=$ 500 fb$^{-1}$ per year (such as the recently
proposed TESLA facility) will detect a Higgs boson signal regardless of the
complexity of the Higgs sector and of how the Higgs bosons decay.
