Curve fitting methods were developed which promise to be of considerable utility in extracting structural information from X-ray absorption spectra. In principle the extended X-ray absorption fine structure (EXAFS) for a given atom can be analyzed to reveal the radial distances and atomic numbers of those atoms surrounding the absorber. The requisite high-quality X-ray absorption spectra can now be easily and rapidly obtained on solid or solution samples, using synchrotron radiation from the Stanford electron-positron storage ring SPEAR [Stanford Positron Electron Accelerating Ring] at the Stanford Linear Accelerator Center. In order to provide the basis for an understanding of metalloprotein absorption fine structure, data for ferrocene, Co(NH3)63+, Co(OH2)62+ and a variety of Fe porphyrins were analyzed. The procedure used was to fit the EXAFS of known structures with a parameterized, semiempirical function: .SIGMA.iCiK-.beta.i exp(-2.ltbbrac..sigma.i2.rtbbrac.K2) sin (2 Rik + .alpha. (K)); where the sum is over all neighboring atoms, the distance information Ri is contained in the phase term, and the other variables account for the amplitude behavior as described in detail in the text. These parameters are then used in fits on other known structures, and the accuracy of the calculated distances (Ri) is used as a test for the validity of the method. The results of fits on FeIITPP [meso-tetraphenylporphyrin iron (II)], FeIIITPP(SC6H5) [meso-tetraphenylporphyrin (benzenethiolato) iron (III)] and FeTpivPP(N-MeIm)O2 [dioxygen[mono-N-methylimidazole-meso-tetra (.alpha.,.alpha.,.alpha.,.alpha.-O-pivalamidophenyl)porphyrin]iron (II)] indicate that radial distances out to 4 coordination shells in Fe porphyrins can be determined to better than 0.1 .ANG.. For cases where the interest is only in changes in coordination, difference methods of analysis were developed which allow accurate determination of the geometry and distances to small molecules such as dioxygen which can reversibly bind to the metal ion. For oxy and deoxy FeTpivPP(N-Melm), Fe-O distances are determined to better than 0.03 .ANG.. The interpretation of the EXAFS from an unknown structure relies heavily on comparison with model compound data. A library of transferable phase shift and amplitude functions may eventually be compiled, and curve-fitting analysis of the extended fine structure will probably be useful for determining the local structure around specific atomic constituents in metalloproteins and other complex materials.