  We give arguments for the existence of ``radial excitations'' of
gravitational global monopoles with any number of zeros of the Higgs field and
present numerical results for solutions with up to two zeros. All these
solutions possess a de Sitter like cosmological horizon, outside of which they
become singular. In addition we study corresponding static ``hairy'' black hole
solutions, representing black holes sitting inside a global monopole core. In
particular, we determine their existence domains as a function of their horizon
radius rh.
