  We point out that the equivalence theorem, which relates the amplitude for a
process with external longitudinally polarized vector bosons to the amplitude
in which the longitudinal vector bosons are replaced by the corresponding
pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a
more general formulation of this theorem also holds for effective interactions.
The generalized theorem can be utilized to determine the high-energy behaviour
of scattering processes just by power counting and to simplify the calculation
of the corresponding amplitudes. We apply this method to the phenomenologically
most interesting terms describing effective interactions of the electroweak
vector and Higgs bosons in order to examine their effects on vector-boson
scattering and on vector-boson-pair production in $f\bar{f}$ annihilation. The
use of the equivalence theorem in the literature is examined.
