Dipolar diffusion in the glassy and supercooled liquid states of 12 molecular substances and of their linear chain or network polymerized states formed by condensation polymerization at different temperatures and times have been studied by measuring the dielectric absorption for a fixed ac frequency of 1 kHz. The study showed that as the extent of polymerization increased with increasing isothermal temperature of polymerization, the sub-T-g relaxation peak due to localized molecular motions in the molecular state became gradually extinct, and a corresponding peak at a higher temperature evolved and reached its maximum height. The temperature of the sub-T-g relaxation peak in the polymerized state differed from that of the alpha-relaxation peak of the supercooled molecular liquid by as much as 70 K, but, in several cases, the two temperatures were similar. Reasons for the latter occurrence are given in phenomenological terms, It is concluded that the localized relaxation modes of the polar segments of the macromolecule are not related to the modes of molecular diffusion in the monomeric liquid state above its T-g. The localized relaxation characteristic of the glassy molecular state persists in the incompletely polymerized state, where it is seen as a gamma-relaxation.