  We use the multimonopole moduli space as a tool for studying the properties
of BPS monopoles carrying nonabelian magnetic charges. For configurations whose
total magnetic charge is purely abelian, the moduli space for nonabelian
breaking can be obtained as a smooth limit of that for a purely abelian
breaking. As the asymptotic Higgs field is varied toward one of the special
values for which the unbroken symmetry is enlarged to a nonabelian group, some
of the fundamental monopoles of unit topological charge remain massive but
acquire nonabelian magnetic charges. The BPS mass formula indicates that others
should become massless in this limit. We find that these do not correspond to
distinct solitons but instead manifest themselves as ``nonabelian clouds''
surrounding the massive monopoles. The moduli space coordinates describing the
position and $U(1)$ phase of these massless monopoles are transformed into an
equal number of nonabelian global gauge orientation and gauge-invariant
structure parameters characterizing the nonabelian cloud. We illustrate this
explicitly in a class of $Sp(2N)$ examples for which the full family of
monopole solutions is known. We show in detail how the unbroken symmetries of
the theory are manifested as isometries of the moduli space metric. We discuss
the connection of these results to the Montonen-Olive duality conjecture,
arguing in particular that the massless monopoles should be understood as the
duals to the massless gauge bosons that appear as the mediators of the
nonabelian forces in the perturbative sector.
