Layered lithium molybdates of formula Li(x)Mo2O4 have been shown earlier to be promising cathode materials for secondary batteries. Nevertheless, a better understanding of the evolution of their transport properties as a function of Li composition and water intercalation is still required. This paper reviews the recent progress towards this understanding, ac and dc measurements have been used to describe the transport properties of the following compositions: Li1.3Mo2O4, Li02Mo2O4, Li0.5(H2O)1.3Mo2O4. A combined analysis of the Arrhenius plots of conductivity and NMR spectra for the above samples suggests only one type of atomic site, between the MoO2 layers, for the Li ions, in agreement with the results obtained by X-ray crystallographic studies. A similar study of the corresponding sodium phases: Na0.5Mo2O4, Na0.9Mo2O4, Na1.3Mo2O4 and Na0.4(H2O)1.2Mo2O4, is also presented.