Synchrotron X-ray scattering and broad-band dielectric spectroscopy experiments were performed in order to analyze the effect of strain-induced orientation on the structure/segmental dynamics relationship in natural rubber/layered silicate nanocomposites. The presence of interfacial interaction between nanoparticle-polymer matrix is crucial in promoting strain-induced crystallization in NR nanocomposites, as evidenced by the correlation between structural magnitudes and dynamic parameters. In this sense, the addition of nanoclay leads to enhanced crystallinity and lower onset of crystallization, while the segmental relaxation slows down due to the restriction imposed by the anchoring of chain segments into the crystals, with evidence of an amorphous/semicrystalline transition around a strain ratio lambda = 2.5.