  Aims: We characterize a sample of Gamma-Ray Bursts with low luminosity X-ray
afterglows (LLA GRBs), and study their properties. Method: We select a sample
consisting of the 12\% faintest X-ray afterglows from the total population of
long GRBs (lGRBs) with known redshift. We study their intrinsic properties
(spectral index, decay index, distance, luminosity, isotropic radiated energy
and peak energy) to assess whether they belong to the same population than the
brighter afterglow events. Results: We present strong evidences that these
events belong to a population of nearby events, different from that of the
general population of lGRBs. These events are faint during their prompt phase,
and include the few possible outliers of the Amati relation. Out of 14 GRB-SN
associations, 9 are in LLA GRB sample, prompting for caution when using SN
templates in observational and theoretical models for the general lGRBs
population.
