Abstract <p>Specimens of the industrial alloy Ti–6Al–4V, obtained in almost a single-phase micro-grain α&#xa0;state by a special thermo-mechanical treatment, including hot rolling, were studied by mechanical measurements on tensile straining, as well as by X-ray diffractometry, optical, scanning and transmission electron microscopy, before and after testing for low-cycle fatigue (LCF). It was established that the layered arrangement of grains, first of all, in the transverse sections of the specimens, is characterized by the texture “selection” and appropriate distribution of globular α grains over the orientation Burgers’ relationships and twin orientations. Notably layered along crystallographic orientations of α grains, the micro-textured regions that were revealed in the initial alloy are inherited by its specimens under the LCF, with the number of cycles before the failure ~ (2.8–3.6) × 10⁴. During a fractographic study, it was found that the failure of a fine-grained α microstructure at the LCF testing occurs according to the combined cell-facet intragrain-boundary mechanism. The dimpled relief of the surface of fracture correlates with the size and the rounded shape of the primary α grains.</p>