  In generalized Yang-Mills theories scalar fields can be gauged just as vector
fields in a usual Yang-Mills theory, albeit it is done in the spinorial
representation. The presentation of these theories is aesthetic in the
following sense: A physical theory using Yang-Mills theories requires several
terms and irreducible representations, but with generalized Yang-Mills
theories, only two terms and two irreducible representations are required.
These theories are constructed based upon the maximal subgroups of the gauge
Lie group. The two terms of the lagrangian are the kinetic energy of fermions
and of bosons. A brief review of Yang-Mills theories and covariant derivatives
is given, then generalized Yang-Mills theories are defined through a
generalization of the covariant derivative. Two examples are given, one
pertaining the Glashow-Weinberg-Salam model and another SU(5) grand
unification. The first is based upon a $U(3)\supset U(1)\times U(1)\times
SU(2)$ generalized Yang-Mills theory, and the second upon a $SU(6)\supset
U(1)\times SU(5)$ theory. The possibility of expressing generalized Yang-Mills
theories using a five-dimensional formalism is also studied. The situation is
unclear in this case. At the end a list of comments and criticisms is given.
