Dielectric relaxation spectroscopy (DRS) is presented for a family of four aromatic polyamides trying to relate the structure of the lateral groups to the molecular mobility. A prominent sub-T-g, absorption is always seen followed in some cases by remanent dielectric activity at room temperature and a subsequent increase of the loss permittivity. The low temperature relaxation is analyzed in terms of a Fuoss-Kirkwood equation to obtain the broadness and the strength of these relaxations as well as the activation energy (ranging from 10 to 11 Kcal/mol). The low frequency conductive peak shows in each case a half-width higher (1.30) than those corresponding to a single relaxation time peak (1.144). These values of the half-width are an indication of the complex character of these phenomena. A final discussion of the rotational barriers of the lateral chains rules out that such motions are the only molecular origin for the gamma relaxation. Instead, some kind of motion involving the main chain and where the interchain interactions play a significant role should be considered as responsible for that relaxation.