Heteroepitaxial growth of GaN on Ge(111) by molecular beam epitaxy has previously been reported to be feasible. However, structural characterization revealed that these GaN layers consisted of misoriented domains. In this work, it is shown that the formation of domains can be suppressed by increasing the substrate temperature, decreasing the nitrogen flux or increasing the surface step density by using off-oriented substrates. Hereby, the step flow growth is enhanced with respect to 2D nucleation. The suppression of domains significantly improves the crystal quality of the GaN layer. For 47 nm of GaN a (0 0 0 2) and (10 (1) over bar2) omega FWHM value of, respectively, 408 and 935 arcsec is obtained. (C) 2008 Elsevier B.V. All rights reserved.