  The interior geometry of static, spherically symmetric black holes of the
Einstein-Yang-Mills-Higgs theory is analyzed. It is found that in contrast to
the Abelian case generically no inner (Cauchy) horizon is formed inside
non-Abelian black holes. Instead the solutions come close to a Cauchy horizon
but then undergo an enormous growth of the mass function, a phenomenon which
can be termed `mass inflation' in analogy to what is observed for perturbations
of the Reissner-Nordstr{\o}m solution. A significant difference between the
theories with and without a Higgs field is observed. Without a Higgs field the
YM field induces repeated cycles of massinflation -- taking the form of violent
`explosions' -- interrupted by quiescent periods and subsequent approaches to
an almost Cauchy horizon. With the Higgs field no such cycles occur. Besides
the generic solutions there are non-generic families with a Schwarzschild,
Reissner-Nordstr{\o}m and a pseudo Reissner-Nordstr{\o}m type singularity at
$r=0$.
