  We measured the equivalent width of a large set of near-infrared (NIR,
0.8--2.4$ \ \mu$m) line-strength indices in the XShooter medium-resolution
spectra of the central regions of 14 galaxies. We found that two aluminum
indices Al at 1.31 $\mu$m and Al1 at 1.67 $\mu$m and the two CO indices CO1 at
1.56 $\mu$m and CO4 at 1.64 $\mu$m are tightly correlated with the velocity
dispersion. Moreover, the NIR Al and CO1 indices show strong correlations with
the optical Mg2 and Mgb indices, which are usually adopted as
$\alpha$/Fe-enhancement diagnostics. The molecular FeH1 index at 1.58 $\mu$m
tightly correlates with the optical <Fe> and [MgFe]' indices, which are used as
total metallicity diagnostics. The NIR Pa$\beta$ index at 1.28 $\mu$m has a
behaviour similar to the optical H$\beta$ index, which is a diagnostic of mean
age. We defined two new composite indices, <Al> and [AlFeH], as possible
candidates to be used as NIR diagnostics of total metallicity and $\alpha$/Fe
enhancement. The NIR <Al> index has a strong correlation with the optical Mg2
and Mgb indices, while the [AlFeH] index is tightly correlated with the optical
<Fe> and [MgFe]' indices. The distribution of the data points in the NIR
Pa$\beta$-<Al> and Pa$\beta$-[AlFeH] diagrams mimic that in the optical
[MgFe]'-H$\beta$ and the Mgb-<Fe> diagrams, which are widely used to constraint
the properties of the unresolved stellar populations. We concluded that some
NIR line-strength indices could be useful in studying stellar populations as
well as in fine-tuning stellar population models.
