It is well known that the cyclic deformation behavior and dislocation structures of Cu single crystals with different orientations have been systematically investigated and understood. However, there is as yet no general and unequivocal knowledge of the thermal stability of fatigue-induced dislocation structures in Cu single crystals, which is particularly significant for the further improvement of low energy dislocation structure (LEDS) theory. In previous work, the thermal stability of fatigue dislocation structures in 18 41] single-slip and coplanar double-slip Cu single crystals have been reported. For deeply understanding the orientation-dependent thermal stability of fatigue dislocation structures, in the present work, conjugate and [017] critical double-slip-oriented Cu single crystals were cyclically deformed at different plastic strain amplitudes γ_pl up to saturation, and then annealed at different temperatures (300, 500 and 800 ℃) for 30 min, to examine the thermal stability of various fatigue-induced dislocation structures. It was found that an obvious recovery has occurred in various dislocation structures at 300 ℃. At the higher temperatures, e.g., 500 and 800 ℃, a remarkable recrystallization phenomenon takes place together with the formation of many annealing twins. The thermal stability of various dislocation structures produced in fatigued Cu single crystals with different orientations from high to low are on the order of vein structure, persistent slip band (PSB) structure, labyrinth structure and dislocation cells. The annealing twins formed in Cu single crystals with different orientations all develop strictly along the dislocation slip planes, which have been operated under fatigue deformation. The more serious the fatigue-induced slip deformation, the greater the amount of annealing twins would be. Furthermore, an over high annealing temperature, e.g. 800 ℃, would greatly speed up the migration of boundaries of recrystallized grains to restrain the formation of annealing twins, leading to, more or less, the decrease in the amount of twins.