  It is shown that in a formulation of Yang-Mills theory in two dimensions in
terms of $A=if^{-1}\pa f$, $\bar A=i\bar f\bpa\bar f^{-1}$ with $f(z,\bar z)$,
$\bar f(z,\bar z)\in[SU(N_C)]^c$ the complexification of $SU(N_C)$ , reveals
certain subtleties. ``Physical" massive color singlet states seem to exist.
When coupled to $N_F$ quarks the coupling constant is renormalized in such a
way that it vanishes for the pure Yang- Mills case. This renders the above
states massless and unphysical. In the abelian case, on the other hand, the
known results of the Schwinger model are reproduced with no need of such a
renormalization.
  The massless $QCD_2$ theory is analyzed in similar terms and peculiar massive
states appear, with a mass of $e_c\sqrt {N_F \over 2\pi}$.
