Broadband dielectric spectroscopy has been used to characterize in deep the relaxation behavior of novel bio-based aliphatic-aromatic block copolymers based on poly(butylene terephthalate) (PBT) and poly(lactic acid) (PLA). The results indicate that the copolymerization decreases the ability to crystallize of the resulting block copolymer. The [Formula: see text] relaxation of the block copolymers is consistent with this fact exhibiting initially the characteristics features of an amorphous polymeric material cold crystallizing upon heating. The cold crystallization can be easily visualized by dielectric spectroscopy by a discontinuous and abrupt change of the shape parameters of the [Formula: see text] relaxation. The sub-glass dynamics of the block copolymers is complex and be ascribed to a [Formula: see text] relaxation composed of two local modes, [Formula: see text] and [Formula: see text], which can be assigned to the relaxation in PBT of the bond between the ester oxygen and the aliphatic carbon and to the bond between the aromatic ring carbon to the ester carbon, respectively. With increasing amount of the PLA block the crystallinity decreases as well as the activation energy of the [Formula: see text] mode approaching the expected value for amorphous PBT. On the contrary, the activation energy for the [Formula: see text] exhibits an unexpected increase as the amount of PLA increases. This effect has been explained by considering that at lower temperatures the [Formula: see text] mode of PBT is the more significant while at higher temperatures the [Formula: see text] relaxation of the PLA block becomes the dominant one.