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The microstructure evolution during grain growth in magnetically anisotropic materials can be affected by a magnetic field due to an additional driving force for grain boundary motion which arises from a difference in magnetic free energy density between differently oriented grains. Therefore each grain of a polycrystal, exposed to a magnetic field, is inclined to grow or to shrink by a magnetic force depending on the orientation of the respective grain and its surrounding neighbors with regard to the field direction. A theoretical analysis of the grain growth kinetics in the presence of an external magnetic field reveals that magnetically affected grain growth may result in an orientation distribution that favours grains with a lower magnetic free energy density. As it is experimentally demonstrated on polycrystalline zinc, titanium and zirconium, the crystallographic texture in magnetically anisotropic non-magnetic materials can be effectively changed and controlled by means of annealing in a magnetic field. EBSD-analysis revealed that the observed asymmetrical texture after magnetic annealing is due to a large extent to a significant difference in the number of grains that make up different texture components. The results of computer simulations of magnetically affected grain growth in 2-D polycrystals are in a good agreement with theoretical predictions and experimental findings.