  The Cauchy problem for the Yang-Mills system in two space dimensions is
treated for data with minimal regularity assumptions. In the classical case of
data in $L^2$-based Sobolev spaces we have to assume that the number of
derivatives is more than $3/4$ above the critical regularity with respect to
scaling. For data in $L^r$-based Fourier-Lebesgue spaces this result can be
improved by $1/4$ derivative in the sense of scaling as $r \to 1$ .
