  Zero-field muon spin relaxation (ZF-$\mu$SR) measurements were undertaken on
under- and overdoped samples of superconducting YBa$_2$Cu$_3$O$_{6+x}$ to
determine the origin of the weak static magnetism recently reported in this
system. The temperature dependence of the muon spin relaxation rate in
overdoped crystals displays an unusual behavior in the superconducting state. A
comparison to the results of NQR and lattice structure experiments on highly
doped samples provides compelling evidence for strong coupling of charge, spin
and structural inhomogeneities.
