  We present the light-curves and spectra of 24 afterglows that have been
monitored by Fermi-LAT at 0.1-100 GeV over more than a decade in time. All
light-curves (except 130427) are consistent with a single power-law starting
from their peaks, which occurred, in most cases, before the burst end. The
light-curves display a brightness-decay rate correlation, with all but one
(130427) of the bright afterglows decaying faster than the dimmer afterglows.
We attribute this dichotomy to a quick deposition of the relativistic ejecta
energy in the external-shock for the brighter/faster-decaying afterglows and to
an extended energy-injection in the afterglow shock for the
dimmer/slower-decaying light-curves. The spectra of six afterglows (090328,
100414, 110721, 110731, 130427, 140619B) indicate the existence of a harder
component above a spectral dip/ankle at energy 0.3-3 GeV, offering evidence for
an inverse-Compton emission at higher energies, and suggesting that the harder
power-law spectra of five other LAT afterglows (130327B, 131231, 150523,
150627, 160509) could also be inverse-Compton, while the remaining softer LAT
afterglows should be synchrotron. Marginal evidence for a spectral break and
softening at higher energies is found for two afterglows (090902B and 090926).
