The grain growth of thin films of an A1-0.5wt.\%Cu and of an Al-0.5wt.\%Cu-1.0wt.\%Si alloys has been investigated primarily using transmission electron microscopy and X-ray diffraction. Thin films of 1$\mu$m were deposited on the thermally oxidized (100) Si wafer by sputtering technique. These films have been annealed in air-atmosphere for various times at various annealing temperatures. The variations of grain size distribution, mean grain diameter, and standared deviation were measured as function of annealing conditions. Digitized tablet linked with an IBM-PC was used to analyze the grain structures observed in TEM micrographs of plan view. The degree of the preferred orientation was measured using XRD and TEM. Relative peak intensity of $I_{111}$/$I_{200}$ was taken as the measure of the degree of the preferred orientation. In addition, the analysis of selectied area diffraction patterns has also been perfromed in order to directly measure the orientation of the grains. The average grain size of Al-0.5wt.\%Cu thin films in as-deposit condition was measured to be 0.65$\mu$m and its stadnard deviation was measured to be 0.22. Strong (111) preferred orientation was observed from the as-deposit condition. In the case of Al-0.5wt.\%Cu-1.0wt.\%Si thin films, the average grain size was measured to be 0.36$\mu$m, which is distinctively smaller than that in the Al-0.5wt.\%Cu thin films. Standard deviation 0.11 was also distinctively smaller. This is believed to be due to the formation of Si nodules during the deposition. Lesser pronounced (111) texture was observed in the case of an Al-0.5wt.\%Cu-1.0wt.\%Si thin films. The annealing treatment tend to increase the degree of the preferred orientation. In both thin films, the grain growth does not occur until the annealing temperature reaches $\sim 300^\circ C$. A rapid grain growth is observed within 15 minutes of annealing at temperature above $\sim 300^\circ C$. The grain growth proceeds very slowly afterwards. The coccurrence of grain growth above $\sim 300^\circ C$ is believed to be partly related with the dissolution of $Al_2Cu$ precipitates above this temperature. The transition of growth rate at $\sim$15min. could be due to the transition of the mode from 3-dimensional to 2-dimensional grain growth. In the case of an Al-0.5\%Cu-1.0\%Si thin films, a secondary rapid grain growth occurs at a later stage of annealing at above $\sim 500^\circ C$. This is believed to be due to the dissolution of Si precipitates at above $\sim 500^\circ C$. The application of Vaiyda's microstrucural model suggests that the annealing of an Al-0.5wt.\%Cu thin film at $500^\circ C$ reduces the resistance to the electromigration by 1/10 to that of as-deposit condition. In the case of an Al-0.5\%Cu-1.0\%Si thin film, the model predicts that reduces the resistance to the electromigration by the annealing at $500^\circ C$ 1/20 to that of as-deposit condition. This is due to a larger influence of the variation of the standard deviation as compared to that of the average grain size.