The study of poly(n-butyl methacrylate) (PnBMA) by thermostimulated currents has been performed in order to give a better definition: of the molecular mobility when crossing the glass transition. It reveals the existence of two dipolar relaxation modes: alpha, ascribed to the glass-rubber relaxation, and alpha ', which might be the dielectric manifestation of the liquid-liquid transition. The distribution of relaxation times and the evolution of the activation enthalpies when increasing the temperature have been studied by the fractional polarizations technique. It appears that the alpha and alpha ' modes behave differently, showing the crossover from an Arrhenian to a Vogelian behavior. Furthermore, up to T-alpha, the cooperativity of molecular mobility is highlighted by the existence of a compensation law in agreement with Starkweather's criterion, and above T-alpha, results might be explained by the e;existence of an intermediate state neither glassy nor completely liquid.