Muon spin relaxation ((mu)SR) has been used to study the magnetic ordering in PdMn and AgMn dilute alloys representing disordered ferromagnetism, reentrant ferromagnetism, and spin glass order. A theory of static linewidths for both transverse applied field and zero applied field (mu)SR is described for all types of spin order. The temperature dependence of the static linewidth in the spin glass and ferromagnetic phases is consistent with both a mean field theory of disordered magnetism and an inhomogeneous percolation model. Linewidths in paramagnetic AgMn privde the first direct observation of a conduction electron mediated RKKY component to the muon-local moment interaction. In PdMn, muons are excluded from occupying octahedral interstitial sites directly adjacent to Mn impurities. A theory relating muon spin-lattice relaxation to impurity spin correlation times in the paramagnetic and ordered phases is described. All types of magnetic ordering show a rapid slowing down of impurity spin fluctuations just above the ordering temperature. Muon spin-lattice relaxation in both the ferromagnetic and spin glass state is expected to be insensitive to both long wavelength spin waves and to higher frequency localized spin wave-like excitations. The observed spin glass state relaxation is consistent with a phenomenological theory of low-frequency barrier mode excitations.