The influence of a delay time at the maximum temperature on the number of cycles for the macrocrack initiation for two thermal loading programs was investigated for two single-crystal nickel-based superalloys VIN3 and ZhS32. An analytic approximation of a delay time influence was proposed. Comparison of computational results and analytic formula on the base of constitutive equations with the experimental data was performed for considered single-crystal superalloys and showed a good accuracy. Influence of several mechanical constants of nickel alloy on thermal fatigue strength is presented and discussed. The influence of crystallographic orientation of the corset sample on the thermal fatigue durability with delay times for various thermal loading programs and different single-crystal nickel superalloys was investigated.