The starting material, the deformed state, as well as the recrystallised microstructure and texture have been analysed as a function of Zener-Hollomon parameter and strain for two differently heat-treated AlMgSi alloys, deformed in torsion. An interesting and somewhat surprising observation is that the grain size was always higher in the material heat treated to form large Mg2Si particles. Moreover, no indications of PSN effects were observed in any of the materials, even at the highest Zener-Hollomon parameters. This observation was quite unexpected as the highest Zener-Hollomon parameters were well above the typical critical level for which significant PSN effects have been observed in similar alloys. The results have been carefully analysed and possible explanations are discussed.