  Using NACO on the VLT in the imaging mode we have detected an object at a
distance of only 0.7 arcsec from GQ Lup. The object turns out to be co-moving.
We have taken two K-band spectra with a resolution of lambda /Delta lambda=700.
In here, we analyze the spectra in detail. We show that the shape of spectrum
is not spoiled by differences in the Strehl ratio in the blue and in the red
part, as well as differential refraction. We reanalyze the spectra and derive
the spectral type of the companion using classical methods. We find that the
object has a spectral type between M9V and L4V, which corresponds to a Teff
between 1600 and 2500 K. Using GAIA-dusty models, we find that the spectral
type derivation is robust against different log(g)-values. The Teff derived
from the models is again in the range between 1800 and 2400 K. While the models
reproduce nicely the general shape of the spectrum, the 12CO-lines in the
spectrum have about half the depth as those in the model. We speculate that
this difference might be caused by veiling, like in other objects of similar
age, and spectral class. We also find that the absolute brightness of the
companion matches that of other low-mass free-floating objects of similar age
and spectral type. A comparison with the objects in USco observed by Mohanty et
al. (2004) shows that the companion of GQ Lup has a lower mass than any of
these, as it is of later spectral type, and younger. The same is as true, for
the companion of AB Pic. To have a first estimate of the mass of the object we
compare the derived Teff and luminosity with those calculated from evolutionary
tracks. We also point out that future instruments, like NAHUAL, will finally
allow us to derive the masses of such objects more precisely.
