  As we demonstrate in a process independent way, in a nonlinear
parameterization of the scalar sector of the standard model the Dyson summation
of the Higgs self energy can be performed without violating the Ward
Identities. This implies also the Goldstone boson equivalence theorem, in the
limited range of its validity in effective field theories. This proves an
earlier conjecture of Valencia and Willenbrock. Furthermore, the full Higgs
propagator is independent of the gauge parameters. These results are consistent
with the extension of the `gauge flip' formalism for the construction of gauge
invariant classes of Feynman diagrams to loop diagrams. In a nonlinear
parameterization of a 2-Higgs doublet model, the consistent Dyson summation is
possible for all neutral Higgs bosons, but not for the charged scalars.
Explicit examples of the equivalence theorem are discussed both in the minimal
standard model and a two-Higgs doublet model.
