  We study static spherically symmetric dyonic black holes in
Einstein-Yang-Mills-Higgs theory. As for the magnetic non-abelian black holes,
the domain of existence of the dyonic non-abelian black holes is limited with
respect to the horizon radius and the dimensionless coupling constant $\alpha$,
which is proportional to the ratio of vector meson mass and Planck mass. At a
certain critical value of this coupling constant, $\hat \alpha$, the maximal
horizon radius is attained. We derive analytically a relation between $\hat
\alpha$ and the charge of the black hole solutions and confirm this relation
numerically. Besides the fundamental dyonic non-abelian black holes, we study
radially excited dyonic non-abelian black holes and globally regular
gravitating dyons.
