The growth of epitaxial C-60 thin films on mica(0 0 1) by thermal evaporation has been studied in detail by X-ray pole-figure measurements. The influence of the deposition rate, the substrate temperature and the him thickness on the in-plane epitaxial arrangements and the formation of twins has been investigated. It has been demonstrated that the C-60 growth is determined by two independent and equivalent C-60-crystal grain alignments (type-A and type-B). The nearly six-fold symmetry of the mica(001)-substrate surface offers the three-fold fcc-(1 1 1)-oriented C-60-crystal grains two equivalent crystal alignments. A high deposition rate of 0.5 Angstrom/s is responsible for the formation of twins at a substrate temperature of 150 degrees C, which diminishes by a higher substrate temperature of 200 degrees C. By a decrease of the deposition rate down to 0.08 Angstrom/s the twins vanish at a film thickness of 200 nm and at the substrate temperature of 150 degrees C. Under the same sublimation conditions, in addition to the type-A and type-B crystal orientations, the growth of the thin C-60 films starts with a slight fibre texture which does not appear at a larger film thickness.