The aim of this study was to investigate in greater detail the occurrence of geometrical bowing and the average molecular orientation direction in biaxially stretched and annealed film webs and to determine possible causes for these effects at a morphological level. This involved studying the temperature-dependent behavior of annealed and nonannealed film webs and determining the geometrical bowing and average molecular orientation direction across the working width of the film. The average molecular orientation direction was measured offline using a polarimeter and also online using a novel online orientation sensor. It was shown that the geometrical bowing correlates directly with the amount of film shrinkage in machine direction which occurs during annealing in the transverse direction orienter. In addition, a possible explanation is given for the greater increase in the molecular orientation angle at the film edges compared with the geometrical bowing. Good agreement was found between online and offline measurement of the molecular orientation angle. (C) 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 127: 2928-2937, 2013