  We obtained medium-resolution near-infrared spectra of seven young M9.5-L3
dwarfs classified in the optical. We aim to confirm the low surface gravity of
the objects in the NIR. We also test whether atmospheric models correctly
represent the formation and the settling of dust clouds in the atmosphere of
young late-M and L dwarfs. We used ISAAC at VLT to obtain the spectra of the
targets. We compared them to those of mature and young BD, and young late-type
companions to nearby stars with known ages, in order to identify and study
gravity-sensitive features. We computed spectral indices weakly sensitive to
the surface gravity to derive near-infrared spectral types. Finally, we found
the best fit between each spectrum and synthetic spectra from the BT-Settl 2010
and 2013 models. Using the best fit, we derived the atmospheric parameters of
the objects and identify which spectral characteristics the models do not
reproduce. We confirmed that our objects are young BD and we found NIR spectral
types in agreement with the ones determined at optical wavelengths. The
spectrum of the L2-gamma dwarf 2MASSJ2322-6151 reproduces well the spectrum of
the planetary mass companion 1RXS J1609-2105b. BT-Settl models fit the spectra
and the 1-5 $\mu$m SED of the L0-L3 dwarfs for temperatures between 1600-2000
K. But the models fail to reproduce the shape of the H band, and the NIR slope
of some of our targets. This fact, and the best fit solutions found with
super-solar metallicity are indicative of a lack of dust, in particular at high
altitude, in the cloud models. The modeling of the vertical mixing and of the
grain growth will be revised in the next version of the BT-Settl models. These
revisions may suppress the remaining non-reproducibilities.
