Assuming perturbativity up to a high energy scale similar to 10(16) GeV, we
demonstrate that a future e(+)e(-) linear collider operating at root s = 5
00 GeV with integral L = 500 fb(-1) per year (such as the recently proposed
TESLA facility) will detect a Higgs boson signal regardless of the complex
ity of the Higgs sector and of how the Higgs bosons decay. [S0031-9007(99)0
8409-4].