The formation of thin films of CuInS2 by the reactive annealing of Cu-In precursors in H2S atmosphere as a technologically favourable method for large-scale and low-cost production of CuInS2 solar-cell material is investigated. The phase-formation process, as a function of temperature, reaction time, and precursor composition, is studied by means of X-ray diffraction and complementary perturbed gamma-gamma angular correlation measurements. Single-phase p-type conducting CuInS2 films are obtained for the annealing temperatures 400 degrees C and 500 degrees C and precursor compositions In/(In + Cu) ranging from 0.48 to 0.50. The composition range where single-phase CuInS2 is obtained is determined to be a copper- and sulphur-rich region of the phase diagram. Furthermore, the results suggest a three-step model for the phase formation during the reactive annealing process. This includes the intermediate formation of the sulphur-rich binary sulphides CuS and In2S3 which then react to form CuInS2.