The high-temperature deformation mechanisms of a ${alpha}+{eta}$ titanium alloy (Ti-6Al-4V), near-a titanium alloy (Ti-6.85Al-1.6V) and a single-phase a titanium alloy (Ti-7.0Al-1.5V) were deduced within the framework of inelastic-deformation theory. For this purpose, load relaxation tests were conducted on three alloys at temperatures ranging from 750 to $950^{circ}C$. The stress-versus-strain rate curves of both alloys were well fitted with inelastic-deformation equations based on grain matrix deformation and grain-boundary sliding. The constitutive analysis revealed that the grain-boundary sliding resistance is higher in the near-${alpha}$ alloy than in the two-phase ${alpha}+{eta}$ alloy due to the difficulties in relaxing stress concentrations at the triple-junction region in the near-${alpha}$ alloy. In addition, the internal-strength parameter (${sigma}^*$) of the near-${alpha}$ alloy was much higher than that of the ${alpha}+{eta}$ alloy, thus implying that dislocation emission/ slip transfer at ${alpha}/{alpha}$ boundaries is more difficult than at ${alpha}/{eta}$ boundaries.