The structural evolution under uniaxial tension of both Polyamide-11 (PA11) and Polyamide-6 (PA6) crystallized under various crystal forms has been investigated as a function of draw temperature with respect to the Brill transition. The use of in-situ synchrotron two-dimensional wide-angle X-ray diffraction and small-angle X-ray scattering allows to discriminate thermal from mechanical effects, leading to a revisited scheme of the strain-induced phase transitions in polyamides. It is demonstrated that only the H-bonded sheet-like structures transform mechanically into a pseudo-hexagonal form with a random distribution of H bonds around the chain axis. This order-disorder transition occurs during the fibrillar transformation and seems systematically preceded by a twinning mechanism at low deformation. By contrast, the mesophases and the High Temperature forms are mechanically stable, the latter transforming thermally into the H-bonded sheet-like structures as soon as samples are cooled down below the Brill transition temperature.