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Annealing processes in MgB2 films deposited on yttria-stabilized zirconia (YSZ)-buffered Hastelloy substrates were studied by transmission electron microscopy. The MgB2 films with Mg-rich compositions were fabricated at room temperature using a pulsed laser deposition (PLD) method. The as-deposited films do not exhibit clear superconducting transitions, and have inhomogeneous microstructures composed of amorphous regions and a small amount of crystalline MgB2 and MgO with several tens of nm in size. Various sizes of voids are also incorporated within the amorphous regions. After the annealing at 600 or 680°C, the films exhibit clear superconducting transitions. The amorphous regions crystallize into fine grains of MgB2 or MgO 5-50 nm in size. The voids remain in the annealed films and their sizes depend on the annealing condition. Magnesium-and oxygen-rich layers are formed near the MgB2/YSZ interface and the film surface. It is suggested that the finer grains of MgB2 and MgO obtained by the lower-temperature annealing give a larger critical current density under a high magnetic field.