  We consider gauge field theories in $D>4$ following the Wilson RG approach
and show that they possess the ultraviolet fixed points where the gauge
coupling is dimensionless in any space-time dimension. At the fixed point the
anomalous dimensions of the field and vertex operators are known exactly. These
fixed points are nonperturbative and correspond to conformal invariant
theories. The same phenomenon also happens in supersymmetric theories with the
Yukawa type interactions.
