  A theoretical attempt to identify the physical process responsible for the afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the occurrence of thermal emission in the comoving frame of the shock wave giving rise to the bursts. The determination of the luminosities and spectra involves integration over an infinite number of Planckian spectra, weighted by appropriate relativistic transformations, each one corresponding to a different viewing angle in the past light cone of the observer. The relativistic transformations have been computed using the equations of motion of GRBs within our theory, giving special attention to the determination of the equitemporal surfaces. The only free parameter of the present theory is the ``effective emitting area'' in the shock wave front. A self consistent model for the observed hard-to-soft transition in GRBs is also presented. When applied to GRB 991216 a precise fit $(\chi^2\simeq 1.078)$ of the observed luminosity in the 2--10 keV band is obtained. Similarly, detailed estimates of the observed luminosity in the 50--300 keV and in the 10--50 keV bands are obtained. 
On the instantaneous spectrum of Gamma-Ray Bursts