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Near-α Ti-alloys such as TIMETAL® 834 are known for their superior mechanical properties at high temperature, and as such are found in applications where high strength and improved fatigue performance at elevated temperatures (>450°C) are required. However, these alloys can be susceptible to cold-dwell fatigue; a failure mechanism that is not well understood. The present work investigates the strain localisation behaviour during cold creep and the implications it has in terms of dwell susceptibility for two different bi-modal microstructures. Slip traces and strain distributions have been analysed for different material conditions by employing High-Resolution Digital Image Correlation (HRDIC) in combination with orientation mapping. Using this approach, it was possible to distinguish deformation patterns in primary α grains and transformed-β colonies, loaded incrementally to stress levels of 70%, 80% and 90% of the yield stress. Different prior β-grain morphologies didn’t affect the average strains when stresses are low; but strain distributions have been affected by the β-grain morphology. Material with coarse transformation product accumulated larger amounts of plastic strain compared to material with fine transformation product, at the same relative stress levels. At low stress levels, slip bands have been detected both in primary α, as well in the transformed-β phase, cutting through the lamellae, for the material condition with a coarse transformation product; on the other hand, for the material conditions with a fine transformation product, slip bands are localised only in primary α grains at low stress levels. It was also found for both conditions that at low stress levels slip bands are found in grains that are well oriented for basal slip. Based on these observations it is discussed if b-ligaments are significant obstacles to dislocation movement. Finally, the requirement of crystal-plasticity modelling to take into account differences in crystallographic orientations and the elastic and plastic anisotropy of HCP-titanium will be discussed and considered.