  We present low-resolution (R=900) optical (576.1--1,051.1 nm) spectroscopic
observations of 40 candidate very low-mass members in the Upper Scorpius OB
association. These objects were selected using the $I$, $J$ and $K$ photometry
available in the DENIS database. We have derived spectral types and we have
measured H$\alpha$ and NaI doublet (at 818.3 and 819.5 nm) equivalent widths.
We assess the youth of the objects by comparing them to their older
counterparts of similar spectral type in the Pleiades cluster and the field.
Our analysis indicates that 28 of our targets are young very low-mass objects,
and thus they are strong candidate members of the OB association. The other 12
DENIS sources are foreground M dwarfs or background red giants. Our sample of
spectroscopic candidate members includes 18 objects with spectral types in the
range M6.5 and M9, which are likely young brown dwarfs. We classify these
candidates as accreting/non accreting using the scheme proposed by Barrado y
Navascu\'es & Mart\'\i n (2003). We find 5 substellar-mass candidate cluster
members that are still undergoing mass accretion, indicating that the timescale
for accretion onto brown dwarfs can be as long as 5 Myr in some cases.
