The system of interacting Higgs and longitudinal gauge bosons, when the Higgs mass MH varies above 1 TeV, is studied using dispersion relations (N/D method). Models satisfying unitarity and analyticity constraints are constructed and solved exactly. For MH≲0.6 TeV the dispersive and perturbative (tree level) amplitudes are similar. For MH≳1.5 TeV , however, they much differ in structure. For MH≃1.5, in ZZ→ZZ the dispersive amplitudes exceed the perturbative ones by factors 2~4. There are indications of strong interaction effects: In HH→HH there is an ℓ=0 bound state, which can be taken as the Higgs itself; in fact, for MH≃2.5 there is an almost self-consistent solution with respect to the mass, and very roughly with respect to the coupling. There is also some indication of a resonance in ZZ→ZZ, as well as in HH→HH.