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The equivalence theorem states that the leading part of the amplitude for aprocess with external longitudinally polarized vector bosons is given by theamplitude in which the longitudinal vector bosons are replaced by thecorresponding pseudo-Goldstone bosons. The validity of this theorem within thestandard model with a heavy Higgs boson and within the gauged nonlinearsigma-model (in which the Higgs boson is absent) is shown. Furthermore it isexamined to what extent also internal lines other than scalar lines can beneglected. A simple power-counting method is developed which determines theleading diagrams for a given process at an arbitrary loop order. This method isalso applied to effective Lagrangians with additional nonstandard interactionterms of higher dimension (chiral Lagragians).Comment: 17 pages LaTeX, 6 figures as uuencoded eps-file

The equivalence theorem for the heavy-Higgs Standard Model and the gauged nonlinear σ-model