  We used K-band photometry, maximum rotational velocities derived from
Fabry-Perot data and HI observed and predicted masses to study, for the first
time, the K-band, stellar and baryonic Tully-Fisher relations for galaxies in
Hickson compact groups. We compared these relations with the ones defined for
galaxies in less dense environments from the GHASP survey and from a sample of
gas-rich galaxies. We find that most of the Hickson compact group galaxies lie
on the K-band Tully-Fisher relation defined by field galaxies with a few
low-mass outliers, namely HCG 49b and HCG 96c, which appear to have had strong
recent burst of star formation. The stellar Tully-Fisher relation for compact
group galaxies presents a similar dispersion to that of the K-band relation,
and it has no significant outliers when a proper computation of the stellar
mass is done for the strongly star-forming galaxies. The scatter in these
relations can be reduced if the gaseous component is taken into account, i.e.,
if a baryonic Tully-Fisher relation is considered. In order to explain the
positions of the galaxies off the K-band Tully-Fisher relation we favour a
scenario in which their luminosities are brightened due to strong star
formation or AGN activity. We argue that strong bursts of star formation can
affect the B and K-band luminosities of HCG 49b and HCG 96c and in the case of
the latter also AGN activity may affect the K-band magnitude considerably,
without affecting their total masses.
