To explore the role of the olivine grain size and crystal preferred orientation (CPO) on the evolution of the microstructure and the mechanical behaviour of upper mantle rocks up to large strains, we performed axial extension experiments at 1200C, 300MPa confining pressure, and constant displacement rate on three natural peridotites: a fine-grained mylonitic harzburgite with a weak CPO and two coarse-grained well-equilibrated dunites with CPO of variable intensity. Initial flow stresses show a limited range of variation (115-165MPa), with the fine-grained sample showing the highest initial strength. However, the evolution of both mechanical behavior and microstructure differs between fine and coarse-grained peridotites. In the fine-grained harzburgite, necking resulted in decrease in the apparent differential stress. Focusing of strain and stress produced increase of the olivine recrystallized fraction and decrease of the recrystallized grain size in the neck. Analysis of the final stress and strain in the neck indicates softening due to evolution of the microstructure and CPO. In contrast, necking of the coarse-grained samples produced weak or no decrease in the apparent differential stress. This implies hardening, consistently with the increase in bulk intragranular misorientation and final stresses in the neck similar or higher than initial ones. Coarse-grained dunites deformed heterogeneously. Crystals well oriented to deform by dislocation glide became elongated, whereas those in hard orientations remained almost undeformed. In the neck, stress and strain concentration resulted in formation of kinks in hard crystals and dynamic recrystallization in soft crystals. We interpret the more effective strain-induced softening of the fine-grained peridotite as due to easier dynamic recrystallization, probably due to the higher proportion of grain boundaries acting as nucleation sites.