  The Cauchy problem for the Yang-Mills system in three space dimensions with
data in Fourier-Lebesgue spaces $\hat{H}^{s,r}$ , $1 < r \le 2$ , is shown to
be locally well-posed, where we have to assume only almost optimal minimal
regularity for the data with respect to scaling as $r \to 1$ . This is true
despite of the fact that no null condition is known for one of the critical
quadratic nonlinearities, which prevented by now the corresponding result in
the classical case $r=2$ with data in standard Sobolev spaces.
