The dynamic behavior of a series of polymers based on 2,6-naphthalenedicarboxylic acid where the chemical structure of the monomer has been systematically modified was studied. The effect of the different chemical structure of the monomeric unit on the subglass dynamics has been evaluated. The P relaxation has a complex character. The slowest subglass relaxation, labeled as beta* relaxation, is directly related to motions of the naphthyl moiety. However, the observed variations of the position of this relaxation, compared with analogues' more rigid polymers, indicate a certain degree of cooperativity of the subglass dynamics.