[en] Results of a leptonic jet model for the prompt emission and early afterglows of GRBs are presented. The synchrotron component is modeled with the canonical Band spectrum and the synchrotron self-Compton component is calculated from the implied synchrotron-emitting electron spectrum in a relativistic plasma blob. In the comoving frame the magnetic field is assumed to be tangled and the electron and photon distributions are assumed to be isotropic. The Compton-scattered spectrum is calculated using the full Compton cross-section in the Thomson through Klein-Nishina using the Jones formula. Pair production photoabsorption, both from ambient radiation in the jet and from the extragalactic background light (EBL), is taken into account. Results are presented as a function of a small set of parameters: the Doppler factor, the observed variability timescale, the comoving magnetic field, the peak synchrotron flux, and the redshift of the burst. Model predictions will be tested by multiwavelength observations, including the Swift and GLAST satellites, which will provide unprecedented coverage of GRBs