Low cycle fatigue (LCF) and creep-fatigue (CF) interaction behavior of 720Li alloy were studied for the first time at 720 °C with different values of total strain amplitudes (Δεt/2) and hold time (HT). At Δεt/2 = 0.6%, CF life is less than LCF life. However, at Δεt/2 = 0.44, 0.48 and 0.55% CF life increased with increase in HT. Texture analysis of specimen tested at Δεt/2 = 0.44%, revealed that initial loading direction ǁ [11¯1] found to be rotated: (i) [21¯1] in LCF condition; and (ii) [11¯0] and [01¯1] in the CF condition predominantly. Notably, texture components developed in the CF specimens tested at Δεt/2 = 0.6% is quite similar to that in the LCF specimen tested at Δεt/2 = 0.44%. Development of [21¯1] texture component is due to multi planner slip (i.e. octahedral and cubic plane slip) under the influence of compressive load which is also confirmed by viscoplastic-simulation. Evolution of [21¯1] texture component leads to greater extent of inter crystalline cracks due to latent strain hardening and strain incompatibility between adjacent grains. Further, high static interfacial energy of annealing twin boundaries, confirmed through five-parameter stereological analyses, in LCF specimen tested at Δεt/2 = 0.44% and CF specimen tested at Δεt/2 = 0.6% resulted annealing twin boundary cracking. In contrast, evolution of low modulus texture components (i.e. [11¯0] & [01¯1]) has been inferred to be responsible for higher cyclic life in CF specimen tested at Δεt/2 = 0.44% and LCF specimen tested at Δεt/2 = 0.6%.