Features of the relaxation behavior of an aromatic polyamide-imide and a composite with nanotubes of magnesium silicate with the structure of chrysotile have been studied by dynamic mechanical analysis, dielectric spectroscopy, and differential scanning calorimetry. Two secondary relaxation (β1 and β2) transitions have been found, the activation energies of these processes have been determined, and the solvent effect on the cooperativeness degree has been studied. Changes in the value of the apparent activation energy of the β1-process caused by the subsequent heating of polymeric and composite samples have been analyzed according to the Starkweather procedure. It has been shown that, as the solvent is released from the polyamide-imide film, the polymer exhibits increasing local mobility, which are predetermined by the structure of the molecular unit. Using the GAMESS software, we have assumed the most probable dimer conformations that correspond to two repeating units of the polyamide-imide molecule.