  We discuss how to describe U(N)-monopoles on the Schwarzschild and
Reissner-Nordstr\"om black holes by the parameters of the moduli space of
holomorphic vector bundles over S^2. For N = 2,3 we obtain such a description
in an explicit form as well as the expressions for the corresponding monopole
masses. This gives a possibility to adduce some reasonings in favour of
existence of both a 'fine structure' for black holes and the statistical
ensemble tied with it which might generate the black hole entropy. Also there
arises some analogy with the famous K-theory in topology.
