  In two-dimensional Yang-Mills and generalized Yang-Mills theories for large
gauge groups, there is a dominant representation determining the thermodynamic
limit of the system. This representation is characterized by a density the
value of which should everywhere be between zero and one. This density itself
is determined through a saddle-point analysis. For some values of the parameter
space, this density exceeds one in some places. So one should modify it to
obtain an acceptable density. This leads to the well-known Douglas-Kazakov
phase transition. In generalized Yang-Mills theories, there are also regions in
the parameter space where somewhere this density becomes negative. Here too,
one should modify the density so that it remains nonnegative. This leads to
another phase transition, different from the Douglas-Kazakov one. Here the
general structure of this phase transition is studied, and it is shown that the
order of this transition is typically three. Using carefully-chosen parameters,
however, it is possible to construct models with phase-transition orders not
equal to three. A class of these non-typical models are also studied.
