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 <$E theta~>>~0,07>, Dy overlayers deposited at low temperatures (<$E T~approx~100~roman K >) are ordered and keep their structure upon annealing up to 350 - 600 K. Near <$E theta~=~0,68 >, the overlayers are stable to high-temperature annealing (<$E T sub a~=~1000~roman K >) as well, whereas the denser films are metastable and transform to more stable ordered structures. An unusual annealing effect is found for <$E theta~<<~0,58 >: the initially ordered metastable phases are replaced by phases having no extended order, which are assumed to be two-dimensional glasses.

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