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Nuclear magnetic resonance measurements are reported for two systems: La1-xSrxCoO3 and La2−xSrxCuO4. The local nature of NMR finds local order at temperatures well above the bulk phase transitions of these compounds. This demonstrates the important role of fluctuations in strongly correlated systems. La1−xSrxCoO3: Nanoscale inhomogeneity in La1−xSrxCoO3) has been investigated in single crystal samples for 0.05≤x≤0.30 using 139La and 59Co NMR to probe local magnetization. Ferromagnetism is only exhibited above the metal-to-insulator (MIT) critical concentration, xC. However, over the entire doping range, the single crystals exhibit an unusually broad and asymmetric distribution of hyperfine fields, evidencing (local) magnetic cluster formation that persists to temperatures as high as 200 K, well above the glass transition reported from bulk magnetization. Above xC the asymmetry decreases rapidly with increasing doping as magnetic clusters overlap to give rise to long-range ferromagnetism. The key features of the spectra are reproduced by a simple model in which Sr dopants trigger magnetic cluster formation. Relaxation measurements at various locations in the magnetic clusters show the correlation times of the fluctuating hyperfine fields becomes very slow on the edges of a magnetic cluster due to large amounts of disorder. Below the MIT the system is made of two regions, a) the very weakly magnetic regions outside a cluster where Co3+ ions undergo spin-state transitions nearly identical to the parent compound, and b) the disorder spin-glass regions made up of the magnetic clusters. The clusters grow slowly with doping and see only a slowly changing density of states until they begin to merge at x=0.10 where they grow rapidly and the carrier density drops. La2−xSrxCuO4: At intense magnetic fields (30T)17O NMR exhibits two distinct signatures for planar oxygen sites instead of the singular site expected from the identical lattice symmetry at oxygen sites in the copper-oxygen plane for underdoped, orthorhombic La2−xSrxCuO4. Analysis of Knight shift, linewidth, quadrupolar splitting and spectral asymmetry indicates that roughly 75% of the planar oxygens evidence antiferromagnetically-correlated nearest neighbor Cu moments at temperatures below ∼30 K, consistent with previous reports. A second planar oxygen site first observed in this study shows that there are mobile holes on roughly 25% of the planar oxygen sites that (a) suppress magnetism for all T<300K and>(b) show a Knight shift that drops to zero below ∼60 K, evidencing pair formation at a temperature well above the superconducting transition temperature (∼4 K at 30 T) and more than twice the superconducting transition temperature at zero magnetic field.