Load-controlled fatigue and dwell-fatigue tests were run at room temperature on tubular specimens of Ti6Al4V under combined tension and internal pressure in a proportion producing nearly equibiaxial loading, or under internal pressure alone. The maximum stress ranged from 75% to 92% of the 0.2% yield stress (92 to 112% of the cyclic yield stress) and the R-ratio was zero, so that no cyclic plasticity occurred. Biaxial loading had a positive influence on fatigue lives. In dwell-fatigue, creep was observed in the longitudinal and transverse directions and was associated with a reduction in fatigue lives that increased with the loading range. SEM observations of damage mechanisms as well as finite element computations of stress and strain fields were performed to analyse and discuss these results.