Experimental studies of the phase transitions in the adsorption system Li/Mo(112) are presented. This system is a model system for highly anisotropic interactions. From measurements of the half-widths of the low-energy electron diffraction spot profiles a phase diagram is derived for the whole submonolayer region of coverage in the temperature range 100–500 K. The commensurate low-coverage phases below θ=0.6 form chains normal to the troughs of the substrate. The commensurate p(4×1) phase, which is completed at a coverage, θ, of 0.25 monolayers (ML), seems to be truly long range ordered, whereas the p(2×1) phase at θ=0.5 still contains domain boundaries even at the lowest temperature of 100 K. Both undergo temperature-driven order-disorder phase transitions. In contrast, the incommensurate phases existing in the coverage range θ=0.66–0.90 form chains along the troughs, which are only weakly coupled normal to the troughs of the substrate. These phases exhibit two coverage-driven phase transitions from rectangular to oblique units cells and back at critical coverages of 0.66 and 0.85, respectively, and represent floating solids. As a function of temperature, they undergo a two-dimensional melting transition. Close to the critical coverages, the melting temperatures show a sharp drop below the temperature range accessible in our experiments. Both functional dependences of the angular deviation from 90° and of the melting temperature on coverage are in good agreement with a phenomenological theoretical model, assuming an instability of the shear modulus of the adsorbate unit cell at the critical coverages.