The temperature. dependence of the alpha-relaxation time out of equilibrium has been investigated by means of dielectric relaxation in a series of fragile glass, formers including several polymers. The influence of physical aging on this behavior has also been studied. The experimental results have been quantitatively compared with the predictions of the Adam-Gibbs equation. It has been found that, whereas for small molecule glass formers the experimental values of the apparent activation energy agree quite well with the prediction of the Adam-Gibbs equation, for polymers the experimental activation energy, values are systematically higher. Moreover, whereas for small molecule glass formers the experimental values of the apparent activation energy remains essentially unaffected by physical aging, for polymers a pronounced reduction of the experimental apparent activation energy is observed. These results are found to be consistent with the Adam-Gibbs equation if a significant temperature variation of the configurational entropy in the investigated temperature range would occur for nonannealed polymers, being the possible variation hardly noticeable for the small molecules. With this assumption, all the obtained results would support the validity,of the Adam-Gibbs equation for describing the temperature dependence of the time scale of the alpha-relaxation also out of equilibrium, at least for fragile glass formers. (C) 2004 American Institute of Physics.