A general approach for simulation of EPR spectra of mixed-valence dimanganese complexes and proteins is presented, based on the theory of Sage et al. (J. Am. Chem,Soc. 1989, 111, 7239-7247),which overcomes limitations inherent in the theory of strongly coupled ions. This enables explanation of "anomalous" spectral parameters and extraction of accurate g tensors and Mn-55 magnetic hyperfine tensors from which the spatial distribution of the unpaired spin density, the electronic configuration, and ligand field parameters have been obtained, This is used to analyze highly accurate simulations of the EPR spectra, obtained by least-squares fits of two mixed valence oxidation states, from a series of dimanganese(II,III) and dimanganese(III,IV) complexes and from the dimanganese catalase enzyme, MnCat(II,III) and MnCat(III,IV), from Thermus thermophilus. The sign of the Mn-55 dipolar hyperfine anisotropy (Delta a) reveals that the valence orbital configuration of the Mn(III) ion in MnCat(III,IV) and all dimanganese(III,IV) complexes possessing sterically unconstrained bis(mu-oxo) bridges is d(pi)(3)(d(22))(1) with the antibonding d(22) electron oriented perpendicular to the plane of the Mn-2(mu-O)(2) rhombus. This accounts for the strong Mn-O bonding and slow ligand exchange kinetics widely observed. The asymmetry of the spin density of Mn(III) increases substantially from Delta a/a(iso) = 0.27 in MnCat(III,IV) to 0.46 in MnCat(II,III), reflecting a change in manganese coordination. Comparison with model complexes suggest this may be due to protonation and opening of the (mu-O)(2) bridge upon reduction to yield a single mu-OH bridge. The presence of strong Mn-O bonding in an unreactive (mu-O)(2) core of MnCat(III,IV) offers a plausible explanation for the 10(12) slower kinetics of peroxide dismutation compared to what is observed for the physiologically important oxidation state MnCat(II,II). For the dimanganese(II,III) oxidation state, the theory also provides the first explanation for the anomalously large (similar to 30%) Mn-55(II) hyperfine anisotropy in terms of admiring of the S = 3/2 excited state into the ground state (S = 1/2) via the zero-freld splitting interaction of Mn(III). This "transferred" anisotropy obscures the otherwise typical isotropic high-spin 3d(5) orbital configuration of Mn(II). An estimate of the ratio of the zero-field splitting to the Heisenberg exchange interaction (D/J) is obtained. The theory also explains the unusuarl 12-line EPR spectrum for a weakly coupled dimanganese(III,IV) complex (Larson et al. J. Am. Chem. Sec. 1992, 114, 6263-6265), in contrast to the typical 16-line "multiline" spectra seen in strongly coupled dimanganese(III,IV) complexes. The theory shows this is due to a weak J = -10 cm(-1) which results in a D/J ratio approaching unity and not to unusual intrinsic magnetic hyperfine parameters of the Mn ions.