AlxGa1-xAs hetero-epitaxial layers have been realised from undersaturated Al/Ga/GaAs melt using liquid-phase epitaxy (LPE). We have not observed any change of layer thickness after a certain period of isothermal contact of GaAs(100) substrate with an undersaturated melt. Theoretically, we have demonstrated that a small change in the interfacial energy between the substrate and melt provides the driving force for AlxGa1-xAs heteroepitaxial layers. AFM image reveals the atomic fiat terraces running parallel to the (110) direction. The grading of aluminium composition from surface to interface has been confirmed using photoelectron spectroscopy. Details on the growth conditions and on the characterisation results are presented.