The structure-dynamics relationships in random copolymers of poly(trimethylene terephthalate) and poly(neopenthyl terephthalate) (PTT PNT) have been investigated by means of X-ray scattering and dielectric loss spectroscopy experiments. The results show that the incorporation of neopenthyl terephthalate units into PTT chain decreases the ability to crystallize of the resulting copolymers as compared to that of PTT. The subglass dynamics of the copolymers is characterized by the existence of two processes, beta(1), and beta(2). We propose that the high frequency secondary relaxation beta(1), is associated with the most flexible part of the repeat unit, whereas the low frequency mode beta(2)has been assigned to the carbon of the ester groups linked to the aromatic ring. On the contrary the poly(neopenthyl terephthalate) (PNT), presents only one subglass process, that we hypothesize to have the same origin of the relaxation of beta(2) relaxation in PTT. The segmental dynamics for the amorphous specimens, characterized by the alpha-process, follows an expected molar ratio behavior. A particular effect characterized by a reduction of the segmental mobility induced by the presence of the counits is observed in the copolymers.