  We study the molecular gas properties of high-$z$ galaxies observed in the
ALMA Spectroscopic Survey (ASPECS) that targets a $\sim1$ arcmin$^2$ region in
the Hubble Ultra Deep Field (UDF), a blind survey of CO emission (tracing
molecular gas) in the 3mm and 1mm bands. Of a total of 1302 galaxies in the
field, 56 have spectroscopic redshifts and correspondingly well-defined
physical properties. Among these, 11 have infrared luminosities
$L_{\rm{}IR}>10^{11}$ L$_\odot$, i.e. a detection in CO emission was expected.
Out these, 7 are detected at various significance in CO, and 4 are undetected
in CO emission. In the CO-detected sources, we find CO excitation conditions
that are lower than typically found in starburst/SMG/QSO environments. We use
the CO luminosities (including limits for non-detections) to derive molecular
gas masses. We discuss our findings in context of previous molecular gas
observations at high redshift (star-formation law, gas depletion times, gas
fractions): The CO-detected galaxies in the UDF tend to reside on the
low-$L_{\rm{}IR}$ envelope of the scatter in the $L_{\rm{}IR}-L'_{\rm{}CO}$
relation, but exceptions exist. For the CO-detected sources, we find an average
depletion time of $\sim$ 1 Gyr, with significant scatter. The average
molecular-to-stellar mass ratio ($M_{\rm{}H2}$/$M_*$) is consistent with
earlier measurements of main sequence galaxies at these redshifts, and again
shows large variations among sources. In some cases, we also measure dust
continuum emission. On average, the dust-based estimates of the molecular gas
are a factor $\sim$2-5$\times$ smaller than those based on CO. Accounting for
detections as well as non-detections, we find large diversity in the molecular
gas properties of the high-redshift galaxies covered by ASPECS.
