Molecular simulation studies of two polyphosphazene polymers including poly[bis(2,2,2-trifluoroethoxy)phosphazene] (PTFEP) and poly[bis(3-methylphenoxy)phosphazene] (PBMP) are presented in this dissertation. Self-diffusion and sorption of seven gases (He, H 2 , O 2 , N 2 , CH 4 , CO 2 , and Xe) in PTFEP have been investigated by molecular dynamics and Grand Canonical Monte Carlo (GCMC) simulations of two amorphous cells and the alfa-orthorhombic crystalline supercell. In the case of the MD simulation of diffusion coefficients, values obtained for both amorphous and crystalline PTFEP are comparable and agree with experimental values obtained for semicrystalline samples. Diffusion coefficients follow a linear correlation with the square of effective diameter of gas molecules according to the correlation of Teplyakov and Meares. On the other hand, solubility coefficients obtained from GCMC simulation of the amorphous cells are approximately four to five times higher than would be expected on the base of the amorphous content of the experimental semicrystalline samples alone. The results suggest that while the crystalline domains in semicrystalline PTFEP samples do not reduce gas diffusivity they significantly reduce gas solubility. A new gas solubility correlation that includes both the Lennard-Jones potential well depth parameter, ε/κ, and the Flory interaction parameter, χ, successfully correlates gas solubility coefficients for all gases including CO 2 . The elevated CO 2 solubility coefficients above the linear correlation of Teplyakov and Meares were attributed to a quadrupole-dipole interaction with the trifluoroethoxy groups of PTFEP by ab initio molecular orbital calculations of CO 2 and model compounds (CH 4 , CH 3 CH 3 , CH 3 CH 2 CH 3 , CF 4 , CF 3 CH 3 , and CF 3 CH 2 CH 3 ). In addition, molecular dynamics simulations of an alfa-supercell indicated that the mesophase transition is associated with a conformational change from the planar cis-trans conformation of the PTFEP backbone in the crystalline supercell to a higher-energy, lower-ordered structure in the mesophase. In the study of PBMP as potential direct methanol fuel cell membranes, the structures, equilibrium water swelling, methanol and water self-diffusion coefficients, and proton conductivity of sulfonated PBMP (crosslinked and non-crosslinked) have been simulated by molecular dynamics methods using a modified COMPASS force field. Both the equilibrium water swelling and the densities obtained for hydrated PBMP cells agree with the experimental values. In addition, the results of self-diffusion coefficients showed that methanol self-diffusion is only affected by the extent of crosslinking but self-diffusion of the hydronium ion is not affected. The results of proton conductivity suggest that at low hydration levels, proton and hydronium ion diffusion coefficients are both very low and the polymer is non-conducting; however increasing water content results in both greater hydronium ion diffusion and higher proton conductivity.