  We have been conducting an imaging survey to detect host galaxies of
radio-quiet QSOs at high redshift (z = 2), in order to compare them with those
of radio-loud objects. Six QSOs were observed in the R passband with the
auxiliary port of the 4.2m WHT of the {\it Observatorio de Roque de los
Muchachos} indir August 1994. The objects were selected to be bright (M(B) <
-28$~mag) and have bright stars in the field, which could enable us to define
the point spread function (PSF) accurately. The excellent seeing of La Palma
(<0.9 arcsec thoughout the run) allowed us to detect extensions to the nuclear
PSFs around three (one radio-loud and two radio-quiet) QSOs, out of 4 suitable
targets. The extensions are most likely due to the host galaxies of these QSOs,
with luminosities of at least 3-7% of the QSO luminosity. The most likely
values for the luminosity of the host galaxies lie in the range 6-18% of the
QSO luminosity. Our observations show that, if the extensions we have detected
are indeed galaxies, extraordinary massive and luminous galaxies are not only a
characteristic of radio-loud objects, but of QSOs as an entire class.
