When is a Higgs THE Higgs?

The one-Higgs-doublet standard model is necessarily incomplete because of the triviality of the scalar symmetry-breaking sector. If the Higgs mass is approximately 600 GeV or higher, there must be additional dynamics at a scale $\Lambda$ which is less than a few TeV. In this case the properties of the Higgs resonance can differ substantially from those predicted by the standard model. In this talk we construct an effective Lagrangian description of a theory with a non-standard Higgs boson and analyze the features of a theory with such a resonance coupled to the Goldstone Bosons of the breaking of $\su$.