We have applied ab initio random structure searching to study the structure, stability and hydrogen storage properties of monolayer TiS2 coated with Li and small Li2O clusters. For the low Li covered system we found a complex adsorption mechanism: some hydrogen molecules were adsorbed due to polarization with Li, others due to polarization with S near the surface of TiS2. The peculiarities of the interaction of the H-2 molecules with each other and the preferred adsorption sites allowed us to formulate a series of recommendations that can be useful when selecting the material for the most effective support. Moreover, the findings also show that the storage capacity of this system can reach up to 9.63 wt%, presenting a good potential as hydrogen storage material. As for the Li2O clusters supported on TiS2, we found that the polarization of the Li-O bond increases upon the adsorption of the Li2O nanocluster. Moreover, the polarized Li-S bonds appear in addition to the already existing Li-O bonds. All this is possible due to the extraction of 1.46 electrons from the S atom of the substrate by O atom of the cluster, and should contribute to an increase in both the adsorption energy and the maximum capacity. The adsorption energies of H-2 for the systems studied here are within 0.11-0.16 eV/H-2 which is a recommended range for reversible hydrogen physisorption under standard test conditions. This study may stimulate experimental efforts to check the claims of high-capacity, stable and reversible hydrogen adsorption reported here. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.