  This paper is devoted to investigating the nonlinear non-abelian Yang-Mills
black holes. We consider three Born-Infeld, exponential, and logarithmic
nonlinear Yang-Mills theories with $SO(n-1)$ and $SO(n-2,1)$ semi-simple
groups, which n is the dimension of spacetime, and obtain a new class of
nonlinear Yang-Mills (NYM) black hole solutions. Depending on the values of
dimension $n$, Yang-Mills charge $e$ and the mass $m$ and nonlinear parameters
$\beta$, our solutions can lead to a naked singularity, a black hole with two
horizons, an extreme or a Schwarzschild-type black hole. We also investigate
the thermodynamic behaviors of the NYM black holes. For small charge values,
the NYM solutions may be thermally stable in the canonical ensemble, if we
consider an AdS spacetime with spherical $k=+1$ and hyperbolic $k=-1$
coordinates or a flat one with $k=+1$. However, there are no stable regions in
the grand canonical ensemble in higher dimensions. For the NYM black hole, we
observe a reentrant phase transition between large and small black holes in the
BI-branch with small $\beta$, which cannot be visible for the nonlinear
Reissner-Nordstrom AdS black hole in the higher dimension. For the limit
$\beta\rightarrow\infty$, the critical ratio $\frac{P_{c} v_{c}}{T_{c}}$ tends
to the constant value $3/8$ for each dimension $n$, while it depends on the
dimension for the case of nonlinear electrodynamics black holes.
