  I calculate spectral evolution series for pulses of GRBs, in the BATSE
spectral range, for continuous particle injection and cooling by synchrotron,
inverse Compton, and adiabatic expansion. The hydrodynamic properties of the
relativistic outflow are homogeneous across the emitting region which is a
conical jet. The flow is viewed at an angle off its symmetry axis; time delays
are taken into account. I discuss the low energy slope part of the spectrum, in
view of the recent claim of photon slopes in bright BATSE bursts that are
inconsistent with the optically thin synchrotron shock model (SSM).
