The method of thermally stimulated currents has been used to study the molecular relaxations in a homologous series of aliphatic polycarbonates varying in monomeric unit size from four to twelve methylene groups. The secondary β relaxation has especially been analyzed considering the complex relaxations often observed at low temperatures in other linear polyesters. In unsubstituted aliphatic polycarbonates, a significant structure in β relaxation is observed only in samples containing water; in perfectly dry samples, it appears that the TSC β peak cannot be resolved in discrete components, even by a fractional polarization technique, and is only characterized by a continuous distribution of relaxation times. On the other hand, in a substituted aliphatic polycarbonate, the β relaxation clearly appears to be structured, showing the important role played by branches for the appearance of a complex relaxation.