An experimental study of the development of molecular orientation in the amorphous phase during the transverse drawing of one-way drawn poly(ethylene terephthalate) films has been carried out. Both the behaviours of phenyl ring normals or chain axes and of fluorescent rigid probes have been considered. The influence of the size of the crystallites in the one-way drawn films has been studied. It is first shown that the phenyl ring normals in the amorphous phase tend to become more perpendicular to the draw direction, as expected. However, there is no marked tendency for the rings to lie in the plane of the film, on the contrary with the crystalline phase. The chain axes, as well as the fluorescent probes, tend to align along the second draw direction. In films possessing initially long crystals, this reorientation appears less efficient at equivalent draw ratios. A memory of the state of the amorphous orientation in the one-way drawn films is observed in the sense that more relaxed one-way drawn films will lead to broader distributions in the final biaxially stretched films.