1. Sedimentation constants and diffusion coefficients have been determined in the ultracentrifuge for four samples of polyamides. 2. On the basis of these examples a fairly rigorous method has been developed for the determination of the molecular weight distribution function for polymers. 3. The experimentally obtained distribution functions have been compared with the theoretical curves required by Plory's theory, and the .invalidity of this theory has been demonstrated. 4. The results obtained are explained as a consequence of the occurrence, durin g the polycondensation process of exchange and degradation reactions between the polymer molecules themselves and between polymer and monomer molecules: as a result of these reactions, the distribution function obtained is fairly narrow. 5. It is pointed out that the widely used methods, based on precipitation from solution, for the fractionation of polymers and the determination of their molecular weight distribution are unsatisfactory. 6. It is concluded that, in solution, polyamides behave as if they consist of compact, not readily penetrated, globular particles; which is an indication of the considerable flexibility of their chains.