By conventional transmission electron microscopy (CTEM) investigations on 2H-AlN films grown by plasma-assisted molecular beam epitaxy (MBE) on Si(001) the influence of the off-axis angle of the substrate surface on the film structure was studied. Three types of Si(001) substrates were used: on-axis, similar to1 degrees, and similar to5 degrees off-axis Si(001) substrates. The AlN layer on an exact oriented Si(001) substrates consists of 3 AIN film domains: two main film domains, AlN(1) and AlN(2), and a small domain AlN(3) at substrate surface defects. Their c-axis orientations are parallel to the c-axis of the substrate: [0001]AlN(1,2,3) parallel to [001]Si. The a-axes of AlN(1) and AlN(2) rotated by 30 degrees to each other: [11 (2) over bar0]AlN(1) parallel to [01 (1) over bar0]AlN(2) parallel to [1 (1) over bar0]Si [3]. The a-axis orientation of AlN(3) is [01 (1) over bar0]AlN(3) parallel to [100]Si. In 2H-AlN films grown on off-axis Si(001) substrates (similar to1 degrees and similar to5 degrees) the ratio between the AlN(1) and AlN(2) film domains changes dramatically as far as a single domain film structure consisting of only AlN(1) is reached. The AlN c-axes of all domains on the off-axis substrates are not parallel to the Si c-axis but tilted by the off-axis angle of the Si(001) substrate (similar to1 degrees respectively similar to5 degrees), i.e. [0001]AlN is parallel to the Si(001) substrate surface orientation.