  We calculate the {\em exact} time-resolved ARPES spectrum of a two-band model
semiconductor driven out of equilibrium by resonant and nonresonant laser
pulses, highlighting the effects of phonon-induced decoherence and relaxation.
{\em Resonant} excitations initially yield a replica of the {\em valence} band
shifted upward by the energy of the exciton peak in photoabsorption. This phase
is eventually destroyed by phonon-induced decoherence: the valence-band replica
lowers in energy by the Stokes shift, locating at the energy of the exciton
peak in photoluminescence, and its width grows due to phonon dressing. {\em
Nonresonant} excitations initially yield a map of the conduction band. Then
electrons transfer their excess energy to the lattice and bind with the holes
left behind to form excitons. In this relaxed regime a replica of the {\em
conduction} band appears inside the gap. At fixed momentum the lineshape of the
conduction-band replica versus the photoelectron energy is proportional to the
exciton wavefunction in "energy space" and it is highly asymmetric. Although
the two-band model represents an oversimplified description of real materials
the highlighted features are qualitative in nature; hence they provide useful
insights into time-resolved ARPES spectra and their physical interpretation.
