The likely mechanism which allows the required migration of functional groups for solid-state polymerization (SSP) of polyamides and polyesters is shown to be interchange reactions. This "chemical diffusion" of functionality has exactly the same mathematical form as that of classical diffusion of small molecules. The consequent model for kinetics of SSP in fine geometries is seen to fit experimental data well. It yields an estimate of the critical distance over which the functionality jumps with each interchange reaction. The critical reaction distance thus obtained, similar to 5 Angstrom, is similar to those determined from diffusion-controlled reactions of small molecules. The profound changes that interchange reactions can produce during SSP in the topology of chain segments in the intercrystalline regions of flexible and semirigid polymers, especially in oriented structures, are revealed.