  We consider the Yang-Mills equations in $(1+d)$-dimensional Minkowski
spacetime. It is known that in the supercritical case, i.e., for $d \geq 5$,
these equations admit closed form equivariant self-similar blowup solutions
\cite{BieBiz15}. These solutions are furthermore conjectured to be the
universal attractors for generic large data equivariant evolutions. In this
paper we partially prove this conjecture. Namely, we show that for all odd $d
\geq 5$ the blowup mechanism exhibited by these solutions is stable.
