  Recent results concerning the internal structure of static
spherically-symmetric non-Abelian black holes in the Einstein-Yang-Mills (EYM)
theory and its generalizations including scalar fields are reviewed and
discussed with an emphasis on the problem of a generic singularity in black
holes. It is argued that in the theories admitting a violation of the naive
no-hair conjecture the structure of singularity is essentially affected by the
"hair roots". This invalidates an image of a non-Abelian black hole as a
Schwarzschild black hole sitting inside the soliton. We give an analytic
description of the generic oscillatory approach to the singularity in the pure
EYM theory in terms of a divergent discrete sequence and show that the mass
function is exponentially growing "in average". The second type of a generic
approach to the singularity in hairy black holes is a "power-law mass
inflation" which is realized in the theories including scalar fields. Both
singularities are spacelike and no Cauchy horizons are met in the full interior
region in conformity with the Strong Cosmic Censorship conjecture. Black holes
violating this conjecture exist only for certain discrete values of the event
horizon radius thus forming a subset of zero measure.
