  We derive the general structure of dimension-six derivative interactions in
the N Higgs doublet models, where Higgs fields arise as pseudo Nambu-Goldstone
modes of a strongly interacting sector. We show that there are several
relations among the dimension-six operators, and therefore the number of
independent operators decreases compared with models on which only SU(2)_L x
U(1)_Y invariance is imposed. As an explicit example, we derive scattering
amplitudes of longitudinal gauge bosons and Higgs bosons at high energy on
models involving two Higgs doublets, and compare them with the amplitudes in
the case of one Higgs doublet.
