Abstract.We have used chemical models that include both gas-phase and grain-surface processes to try to understand the low water and molecular oxygen abundances inferred from SWAS observations towards dense molecular clouds. The models represent an improvement over pure gas-phase chemistries in that they are more realistic, and they are largely successful at reproducing the low O 2 abundances. For cold clouds, such as TMC-1 and L134N, the limits on the H 2 O abundance are met by the models only after relatively long periods of accretion (10 6 -10 7 yr), but we show that ground-based observations of these clouds do not necessarily contradict these ages, especially for L134N. If the upper limits on the H 2 O abundance were to be revised downwards, however, or if water were to be observed in the cold clouds at the same level as in some star-forming regions, then even heavier depletions would be required. For this reason, the low H 2 O abundance observed by SWAS in ρ Oph cannot be reproduced by the models without calculating unphysically low abundances of CO.