  One of the major problems in developing new physics scenarios is that very
often the parameters can be adjusted such that in perturbation theory almost
all experimental low-energy results can be accommodated. It is therefore
desirable to have additional constraints. Field-theoretical considerations can
provide such additional constraints on the low-lying spectrum and
multiplicities of models. Especially for theories with elementary or composite
Higgs particle the Fr\"ohlich-Morchio-Strocchi mechanism provides a route to
create additional conditions, though showing it to be at work requires genuine
non-perturbative calculations. The qualitative features of this procedure are
discussed for generic 2-Higgs-doublet models, grand-unified theories, and
technicolor-type theories.
