We investigate the behavior of the X-ray lightcurves in the afterglow phase of Gamma Ray Bursts (GRB), after taking into account the maximum electron Lorentz factor (gamma_max) as an additional parameter of the problem. First, we treat gamma_max as a free parameter and we examine the lightcurves that one obtains for different values of the ratio gamma_max/gamma_min, where gamma_min is the minimum electron energy. We find that the lightcurves depend strongly on this ratio showing a variety of morphologies, with some having a strong resemblance to the observations. As a next step, we introduce particle acceleration and calculate gamma_max in a self-consistent way by balancing the energy losses with the energy gains of the accelerating electrons. The physical picture corresponds to particles injected at low energies and accelerated in the downstream region of the external GRB shock wave. We simulate that by introducing an acceleration term in the equation that describes the evolution of the electron distribution. We show some first results of the radiated synchrotron photon spectra obtained at various radii of the blast wave. Finally, we discuss possible implications of such 'one-zone' acceleration models for GRB afterglows.