  We present bounds on the Higgs mass in the Standard Model and in the Minimal
Supersymmetric Standard Model using the effective potential with
next-to-leading logarithms resummed by the renormalization group equations, and
physical (pole) masses for the top quark and Higgs boson. In the Standard Model
we obtain lower bounds from stability requirements: they depend on the top mass
and the cutoff scale. In the Minimal Supersymmetric Standard Model we obtain
upper bounds which depend on the top mass and the scale of supersymmetry
breaking. A Higgs mass measurement could discriminate, depending on the top
mass, between the two models. Higgs discovery at LEP-200 can put an upper bound
on the scale of new physics.
