  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 {\em Swift} and {\em
GLAST} satellites, which will provide unprecedented coverage of GRBs.
