  The previously developed renormalizable perturbative 1/N-expansion in higher
dimensional scalar field theories is extended to gauge theories with fermions.
It is based on the $1/N_f$-expansion and results in a logarithmically divergent
perturbation theory in arbitrary high odd space-time dimension. Due to the
self-interaction of non-Abelian fields the proposed recipe requires some
modification which, however, does not change the main results. The new
effective coupling is dimensionless and is running in accordance with the usual
RG equations. The corresponding beta function is calculated in the leading
order and is nonpolynomial in effective coupling. The original dimensionful
gauge coupling plays a role of mass and is also logarithmically renormalized.
Comments on the unitarity of the resulting theory are given.
