Annealing-driven irreversible structural transitions are studied by low-energy electron diffraction in submonolayer Dy films adsorbed on the Mo(112) surface. In a wide coverage range θ>0.07, Dy overlayers deposited at low temperatures (T≈100 K) are ordered and keep their structure upon annealing up to 350–600 K. Near θ=0.68, the overlayers are stable to high-temperature annealing (Ta=1000 K) as well, whereas the denser films are metastable and transform to more stable ordered structures. An unusual annealing effect is found for θ<0.58: the initially ordered metastable phases are replaced by phases having no extended order, which are assumed to be two-dimensional glasses. © 2001 American Institute of Physics.