The present paper is a synthesis of several works performed in the laboratory on mechanisms of the cube texture formation in the Fe-36%Ni alloys which have been studied at a local scale by TEM and EBSD and at a global scale by X-ray and neutron diffraction at the Laboratoire Leon Brillouin (CEA-CNRS) in Saclay. A weak cube component exists after hot rolling, it is quite stable during cold rolling, whereas the copper, aluminium and brass components strengthened with deformation, especially for high reduction (95%). TEM observations of the cold rolled microstructure have shown that the cube bands, are made up of well formed sub-grains while the rest of the deformed matrix is composed of lamellar bands containing a high dislocation density. After a short time annealing of 95% cold rolled sheets, the main mechanism of cube sub-grains growth occurs by direct bulging of prior grain boundaries between cube bands and the matrix into the matrix. Cube sub-grains can also grow, firstly within the cube band through the orientation gradient along the transverse direction, then into the deformed matrix. However, the first mechanism seems more probable because of a favourable difference of deformation stored energy and a high disorientation between the growing cube sub-grain and the deformed matrix which provides the driving force to sub-boundary displacement. For 70% cold rolling, all the components develop during annealing, leading to a weak cube texture. Indeed, the stored energy difference is not sufficient to allow the cube grains to grow more rapidly than the others. Moreover, whatever the deformation amounts, multi-twinning occurring during recrystallisation tends to soften the texture as shown experimentally and by simulation.