  We present new stellar kinematical profiles of four galaxy hosts of active
galactic nuclei, using the CO bandhead around 2.3 micron with the ISAAC/VLT
spectrograph. We find that the nuclear bars or discs, embedded in large-scale
primary bars, have all a decoupled kinematics, in the sense that the maximum of
the rotational velocity occurs in the nuclear region. In three cases (NGC 1097,
NGC 1808 and NGC 5728), the velocity dispersion displays a significant drop at
the nucleus, a rarely observed phenomenon. We also detect kinematical
asymmetries (m=1 mode) along the nuclear bar major-axis of NGC 1808 and NGC
5728, dynamical counterparts of corresponding asymmetries in the surface
brightness. We have derived simple dynamical models in an attempt to fit the
kinematics of each galaxy and reconstruct the full velocity field. For all four
targets, the fits are good, and confirm the presence of the decoupled nuclear
components. These models cannot however reproduce the observed central drop in
the dispersion. We suggest that this drop is due to a transient cold nuclear
disc, fuelled by gas inflow along the bar, that has recently formed new stars.
