The temperature/density dependences of the structure of expanded liquid metals rubidium and caesium have been calculated along the liquid-vapour coexistence curve using the molecular dynamics technique. In contrast to previous simulation studies, we adopt a full density dependent pairwise potential constructed from a highly reliable and accurate non-local model pseudopotential. For both liquid alkali metals, we find that our Fourier-transformed liquid structure factors generally agree quite well with the neutron diffraction data for the wave number approximately 0.6 angstrom-1 and above, whereas for thermodynamic states near the critical point and for wave numbers smaller than approximately 0.6 angstrom-1 we observe large discrepancies which we are unable to account for adequately in the present work. Nevertheless, by examining and comparing the variation of our calculated pair potential as well as the liquid structure factor with temperature/density, our present results provide further information on the validity of nearly-free-electron theory notably for thermodynamic states,approaching the critical regime. Specifically, we conjecture break-down temperatures possibly occurring at T almost-equal-to 1700 K and T almost-equal-to 1600 K for liquid rubidium and caesium metals, respectively.