We study the molecular gas properties of high– z galaxies observed in the ALMA Spectroscopic Survey ( ASPECS ) that targets a \sim 1 arcmin ^ { 2 } region in the Hubble Ultra Deep Field ( UDF ) , a blind survey of CO emission ( tracing molecular gas ) in the 3 mm and 1 mm 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 _ { { } 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 _ { { } IR } envelope of the scatter in the L _ { { } IR } - L ^ { \prime } _ { { } 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 _ { { } H 2 } / 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 .