  The physical, observable spectrum in gauge theories is made up from
gauge-invariant states. The Fr\"ohlich-Morchio-Strocchi mechanism allows in the
standard model to map these states to the gauge-dependent elementary $W$, $Z$
and Higgs states. This is no longer necessarily the case in theories with a
more general gauge group and Higgs sector. We classify and predict the physical
spectrum for a wide range of such theories, with special emphasis on GUT-like
cases, and show that discrepancies between the spectrum of elementary fields
and physical particles frequently arise.
