At high temperatures in air, introducing a dwell period at the peak stress of fatigue cycles promotes time dependent intergranular crack growth which can increase crack growth rates by upto a few orders of magnitude from the rates of transgranular fatigue crack growth in superalloys. It is expected that time dependent intergranular crack growth in nickel-based superalloys may not occur below a critical mechanical driving force, Δ K th−IG , analogous to a fatigue threshold (Δ K th ) and a critical temperature, T th . In this study, dwell fatigue crack growth tests have been carefully designed and conducted on Alloy 720Li to examine such thresholds. Unlike a fatigue threshold, the threshold stress intensity factor range for intergranular crack growth is observed to be highly sensitive to microstructure, dwell time and test procedure. The near threshold crack growth behaviour is made complex by the interactions between grain boundary oxidation embrittlement and crack tip stress relaxation. In general, lower Δ K th−IG values are associated with finer grain size and/or shorter dwell times. Often a load increasing procedure promotes stress relaxation and tends to lead to higher Δ K th−IG . When there is limited stress relaxation at the crack tip, similar Δ K th−IG values are measured with load increasing and load shedding procedures. They are generally higher than the fatigue threshold (Δ K th ) despite faster crack growth rates (d a /d N ) in the stable crack growth regime. Time dependent intergranular crack growth cannot be activated below a temperature of 500 ∘ C.