  Myoglobin (Mb) binds diatomic ligands, like O$_2$, CO, and NO, in a cavity
that is only transiently accessible. Crystallography and molecular simulations
show that the ligands can migrate through an extensive network of transiently
connected cavities, but disagree on the locations and occupancy of internal
hydration sites. Here, we use water $^2$H and $^{17}$O magnetic relaxation
dispersion (MRD) to characterize the internal water molecules in Mb under
physiological conditions. We find that equine carbonmonoxy Mb contains 4.5
$\pm$ 1.0 ordered internal water molecules with a mean survival time of 5.6
$\pm$ 0.5 $\mu$s at 25 $^\circ$C. The likely location of these water molecules
are the four polar hydration sites, including one of the xenon-binding
cavities, that are fully occupied in all high-resolution crystal structures of
equine Mb. The finding that water escapes from these sites, located 17 -- 31
{\AA} apart in the protein, on the same $\mu$s time scale suggests a global
exchange mechanism. We propose that this mechanism involves transient
penetration of the protein by H-bonded water chains. Such a mechanism could
play a functional role by eliminating trapped ligands. In addition, the MRD
results indicate that two or three of the 11 histidine residues of equine Mb
undergo intramolecular hydrogen exchange on a $\mu$s time scale.
