The local structures of the two-dimensional organic/inorganic hybrid nanocomposites, Cu-2(OH)(3)(n-CmH2m+1-COO) (m=0, 1, 7, 8, 9), have been investigated together with Cu-2(OH)(3)NO3, by means of Cu K-edge EXAFS spectroscopy at 20 K. The axial and equatorial Cu-O bond lengths, three kinds of Cu-Cu distances, and their Debye-Waller factors have been determined. The structural parameters for Cu-2(OH)(3)NO3 agree withthose determined by the previous X-ray crystal analyses. The Cu-2(OH)(3)(n-CmH2m+1COO)materials are found to maintain the basic framework of the inorganic layer, but from a microscopic viewpoint, there is a charaxrteristic difference in the local structures between the shorter (m=0, 1) and the longer (m=7-9) alkyl chain materials. While the local structures of the m=0 and 1 materials are very similar to that of Cu-2(OH)(3)NO3, those of m=7-9 exhibit a significant shortening of the axial Cu-O bond length by similar to 0.1 Angstrom, in contrast to little change in the equatorial length. Since the interlayer alkanecarboxylate is always in the axial position, the change is ascribed to the shorfer Cu-carboxylate bond length in the longer chain materials. The structural modifications in the other parts of the layer can be understood as a cooperative motion originating from the change. It is quite unusual that such a large structural modification of an inorganic layer takes place, depending on the intercalated organic molecules, The intralayer structural modification observed in this study is sufficiently large enough to explain the reported drastic change in the magnetic properties between the shorter and longer chain materials.