Nucleation and growth of wurtzite AIN layers on nominal and of axis Si(0 0 I) substrates by plasma-assisted molecular beam epitaxy is reported. The nucleation and the growth dynamics have been studied in situ by reflection high-energy electron diffraction. For the films grown on the nominal Si(0 0 1) surface, cross-sectional transmission electron microscopy and X-ray diffraction investigations revealed a two-domain film structure (AlN1 and AIN) with an epitaxial orientation relationship of [0 0 0 1](AlN) parallel to [0 0 1](Si) and <0 1 (1) over bar 0 > AlN1 parallel to <(2) over bar 1 1 0 > AlN2 \ [1 1 0](Si). The epitaxial growth of single crystalline wurtzite AIN thin films has been achieved on off-axis Si(0 0 1) substrates with an epitaxial orientation relationship of [0 0 0 1](AlN) parallel to the surface normal and <0 1 1 0 > (AlN) parallel to [1 1 0](Si).