  (Abridge) Near-infrared spectroscopy is used to study the kinematics and
excitation mechanisms of the H2 and [FeII] gas in a sample of AGN. The H2 lines
are unresolved in all objects in which they were detected while the [FeII]
lines have widths implying gas velocities of up to 650 km/s. This suggests
that, very likely, the H2 and [FeII] emission does not originate from the same
parcel of gas. Molecular H2 were detected in 90% of the sample, including PG
objects, indicating detectavel amounts of molecular material even in objects
with low levels of circumnuclear starburst activity. The data favors thermal
excitation for the H2 lines. Indeed, in NGC3227, Mrk766, NGC4051 and NGC4151,
the molecular emission is found to be purely thermal. This result is also
confirmed by the rather similar vibrational and rotational temperatures in the
objects for which they were derived. [FeII] lines are detected in all of the
AGN. The [FeII] 1.254mu/Pa-beta ratio is compatible with excitation of the
[FeII] by the active nucleus, but in Mrk 766 it implies a stellar origin. A
correlation between H2/Br-gamma and [FeII]/Pa-beta is found. We confirm that it
is a useful diagnostic tool in the NIR to separate emitting line objects by
their level of nuclear activity. X-ray excitation models are able to explain
the observed H2 and part of the [FeII] emission. Most likely, a combination of
X-ray heating, shocks driven by the radio jet, and circumnuclear star formation
contributes, in different proportions, to the H2 and [FeII] emission. In most
of our spectra, the [FeII] 1.257mu/1.644mu ratio is found to be 30% lower than
the intrinsic value based on current atomic data. This implies either than the
extinction towards the [FeII] emitting clouds is very similar in most objects
or there are possible inaccuracies in the A-values in the [FeII] transitions.
