  Although the Orion Nebula Cluster is one of the most studied clusters in the
solar neighborhood, the evolution of the very low-mass members ($M_* < 0.25 \,
M_\odot$) has not been fully addressed due to their faintness. Our goal is to
verify if some young and very low-mass objects in the Orion Nebula Cluster show
evidence of ongoing accretion using broadband VLT/X-Shooter spectra. For each
target, we determined the corresponding stellar parameters, veiling, observed
Balmer jump, and accretion rates. Additionally, we searched for the existence
of circumstellar disks through available on-line photometry. We detected
accretion activity in three young stellar objects in the Orion Nebula Cluster,
two of them being in the very low-mass range. We also detected the presence of
young transition disks with ages between 1 and 3.5 Myr.
