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Ecosystem stability is one of the main factors maintaining ecosystem functioning and is closely related to temporal variability in productivity. Resistance and resilience reflect tolerance and recovering ability, respectively, of a plant community under perturbation, which are important for maintaining the stability of ecosystems. Generally, heavy grazing reduces the stability of grassland ecosystems, causing grassland degradation. However, how livestock grazing affects ecosystem stability is unclear in alpine steppe ecosystems. We conducted a five-year grazing experiment with Tibetan sheep in a semi-arid alpine steppe on the Qinghai-Tibetan Plateau, China. The experimental treatments included no grazing (NG), light grazing (LG, 2.4 sheep per ha), moderate grazing (MG, 3.6 sheep per ha) and heavy grazing (HG, 6.0 sheep ha). We calculated resistance and resilience of three plant functional groups and ecosystem stability under the three grazing intensities using aboveground primary productivity. The results showed that with increasing grazing intensity, aboveground biomass of each functional group significantly decreased. As grazing intensity increased, the resistance of forbs first increased then decreased. The resilience of graminoids in HG was significantly lower than in LG plots, but the resilience of legumes in HG was higher than in LG and MG plots. The resilience of graminoids was significantly higher than legume and forbs under LG and MG treatments. In HG treatments, resilience of legumes was higher than graminoids and forbs. Ecosystem stability did not change under different grazing intensities, because of dissimilar performance of the resilience and resistance of functional groups. Our results highlight how the differential resistance and resilience of different function groups facilitate the tolerance of alpine steppe to grazing under even a heavy intensity. However, the degradation risk of alpine steppe under heavy grazing still needs to be considered in grassland management due to sharp decreases of productivity. • Grazing intensity have no significant effects on plant resistance. • Resilience of graminoids under heavy grazing was lower than other treatments. • Under heavy grazing, resilience of legumes was higher than graminoids and forbs. • Ecosystem stability did not change under different grazing intensities. [ABSTRACT FROM AUTHOR]