Summary 1. The rolling and annealing structures of an iron-nickel (48 per cent Ni) alloy were investigated by X-rays to obtain a better understanding of the so-called (111) reflections on transmission photograms, originating from those crystal fragments in the recrystallized metal, which deviate in orientation from the predominating cube orientation. 2. In accordance with the observations of other investigators a certain amount of the cubic structure has been found to be present already in the rolled sheet. 3. The crystal fragments in the non-cubic position, after annealing at not too high a temperature, e.g. lower than 900°C, are not to be ascribed to twinning nor can they be described as a superposition of the (111) and (112) orientations, which form the major part of the rolling structure as given by Sachs and Spretnak. The formal description of these crystal fragments (Z-fragments) as twins, rotated 8° about an axis, which is normal to the twinning (111) plane, is in excellent agreement with the experimental data (so-called Z-orientation). 4. The recrystallization structure of very thin sheets of iron-nickel, which according to the foregoing paper is different from the cube orientation, is determined as being composed of Z-fragments and the wide spread cube crystals. 5. Another kind of crystal fragments in the non-cubic orientation is found even after recrystallization at 1100°C. They are in accordance with the foregoing paper to be identified as genuine twins, which have an octahedral plane in common with the cube orientation. 6. The rolling structure of the alloy can be explained for the major part by the above mentioned Z-orientation. 7. The rolling structure is different for inner and outer sheets of the alloy and so is the recrystallization structure. This evidence substantiates the previously mentioned correlation between the rolling structure and the non-cubic orientation of crystal fragments after recrystallization. 8. The degree of perfection of the developed cube orientation is different for an inner and an outer sheet of the alloy on recrystallization; in an outer sheet this orientation is distinctly sharper. The degree of perfection is moreover dependent on the thickness of the sample, it is very low for a very thin sample after recrystallization (see foregoing paper).