  The mass accretion rate is the fundamental parameter to understand the
process of mass assembly that results in the formation of a low-mass star. This
parameter has been largely studied in Classical TTauri stars in star-forming
regions with ages of 1-10Myr. However, little is known about the accretion
properties of young stellar objects (YSOs) in younger regions and early stages
of star formation, such as in the Class0/I phases. We present new NIR spectra
of 17 ClassI/Flat and 35 ClassII sources located in the young (<1Myr) NGC1333
cluster, acquired with the KMOS instrument at the VLT. Our goal is to study
whether the mass accretion rate evolves with age, as suggested by the widely
adopted viscous evolution model, by comparing the properties of the NGC1333
members with samples of older regions. We measured the stellar parameters and
accretion rates of our sample, finding a correlation between accretion and
stellar luminosity, and between mass accretion rate and stellar mass. Both
correlations are compatible within the errors with the older Lupus star-forming
region, while only the latter is consistent with results from ChamaeleonI. The
ClassI sample shows larger accretion luminosities with respect to the ClassII
stars of the same cloud. However, the derived accretion rates are not
sufficiently high to build up the inferred stellar masses, assuming steady
accretion during the ClassI lifetime. This suggests that the sources are not in
their main accretion phase and that most of their mass has already been
accumulated during a previous stage and/or that the accretion is an episodic
phenomenon. We show that some of the targets originally classified as Class I
through Spitzer photometry are in fact evolved or low accreting objects. This
evidence can have implications for the estimated protostellar phase lifetimes.
Further observations are needed to determine if this is a general result.
