It has been shown already that pulsed reactive magnetron sputtering (PMS) allows to deposit crystalline, hard and transparent Al2O3 layers. In this paper, correlations between process parameters, structure and properties of these layers are investigated. The deposition of the layers took place on steel at substrate temperatures (T-s) of 290-770 degrees C. The sputtering power was varied in the range of 11-17 kW, and the substrate bias was 50 V. With increasing substrate temperature and sputtering power, a phase transition takes place from amorphous Al2O3, via gamma-Al2O3 into alpha-Al2O3. At the highest sputtering power, textured gamma-Al2O3 occurs already at T-s approximate to 350 degrees C. The formation of alpha-Al2O3 starts at 670 degrees C, and practically pure alpha-Al2O3 is present at the highest substrate temperature. The substrate bias has a substantial influence on the ratio of the phase fractions of gamma-Al2O3 and alpha-Al2O3. Linked with the formation of crystalline phases is an increase in hardness from 10 up to 22 GPa. In addition, a pronounced increase in residual stresses of the layers can be observed. Pulsed magnetron sputtering permits to coat substrate materials with hard, crystalline aluminum oxide that could not be treated up to now because the substrate temperatures were too high.