Tree-level unitarity constraints on the masses of the Higgs bosons in the g
eneral Two Higgs Doublet Model (THDM) are studied. We first consider the ca
se where the Higgs potential is invariant under a discrete symmetry transfo
rmation, and derive strong constraints on the mass of the lightest CP-even
Higgs boson (M-h) as a function of tan beta. We then show that the inclusio
n of the discrete symmetry breaking term weakens the mass bounds considerab
ly. It is suggested that a measurement of M-h, and tan beta may enable disc
rimination between the two Higgs potentials. (C) 2000 Elsevier Science B.V.
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