One-dimensional iodide-bridged mixed-valence binuclear platinum complexes (the so-called "MMX chains") and their Pt(Ill) dimer precursors were investigated with 1291 Mossbauer spectroscopy. Spectra consisting of two sets of octuplets were observed at low temperatures for a neutral MMX chain complex, Pt-2(dtp)(4)I (dtp = C2H5CS2-), with various charge-ordering states at the Pt dimers, indicating that the charge-ordering state is in an alternate-charge-polarization phase (ACP: center dot center dot center dot [Pt2+- Pt3+]-I0.4--[Pt3+-Pt2+] center dot center dot center dot I0.3- center dot center dot center dot), which is consistent with a previous low-temperature X-ray diffraction study. The estimated valence states of the bridging iodines of (C2H5)(2)NH2](4)[Pt-2(pop)(4)I] (pop= H2P2O52-), with a charge-polarization phase (CP: center dot center dot center dot [Pt2+-Pt3+]-I0.4- center dot center dot center dot [Pt2+-Pt3+]-I0.4-center dot center dot center dot), and [H3N(CH2)(6)NH3](2)[Pt-2(pop)(4)I], with a charge-density-wave phase (CDW: center dot center dot center dot [Pt2+-P3+] center dot center dot center dot I0.3--[Pt3+-Pt3+]-I0.3- center dot center dot center dot), suggest that the covalent bond interaction is dominant in the CDW phase, whereas the Coulomb interaction is dominant in the CP phase. The estimated absolute quadrupole coupling constant (QCC) values for negatively charged MMX chain complexes with pop ligands are larger than those for neutral MMX chain complexes with CH3CS2- (dta) ligands, implying that the Madelung potential formed by the more-negative pop ligands and countercations effectively contributes to the physical properties of the pop system. The three Pt(III) dimer complexes Pt-2(dta)(4)I-2, Pt-2(dtp)(4)I-2, and K-4[Pt-2(pop)(4)I-2] showed almost the same isomer shifts, indicating that the valence state of the iodide ion (I0.5-) depends negligibly on the terminal ligand. The QCC value observed for K-4[Pt-2(pop)(4)I-2] was larger than those for Pt-2(dta)(4)I-2 and Pt-2(dtp)(4)I-2, originating from the anisotropic arrangement of the iodide anions, which form layers lying on the ab plane in the crystal.