A B S T R A C TFree grazing and herding of local breeds have a long tradition in management and conservation of extended grassland habitats such as alkali steppes. However, there is a lack in studies evaluating the effects of grazing types and regimes on the vegetation composition and functional diversity. We selected Artemisia steppes, a widespread type of alkali steppes, to study the changes of vegetation composition and diversity along a grazing intensity gradient. We recorded the cover of vascular plant species, in altogether 150, 2 Â 2-m-sized plots of 15 steppes in 2014. The steppes were managed by free grazing, traditional Hungarian Grey cattle grazing (low, moderate and high intensity), or by heavy grazing (Grey cattle and sheep, and additional donkey grazing). We answered the following questions: (i) How do the species richness, diversity and species evenness change along the increasing intensity of grazing? (ii) How does the grazing affect the functional trait composition along the intensity gradient? (iii) How similar is the composition and diversity of free grazed steppes to the pastoral grazed ones? We detected no significant differences in species richness but a humped-back curve with a peak at the medium grazing intensity was found for the Shannon diversity, evenness and the proportion of subordinated target species. The highest Rao's quadratic entropy was found for low intensity grazing. The lowest scores of multi-trait functional evenness were detected for the medium grazing intensity, while for multi-trait functional divergence both medium and very high intensity displayed low scores. The intensity of grazing was negatively correlated with the plant height and LDMC, while positively with the rosette forming, SLA, thousand-seed weights, terminal velocity and flowering period. Our results suggest that for the highest functional diversity a low intensity traditional cattle grazing is recommended. A medium grazing intensity should be chosen to have the highest proportion of subordinated target species of conservation interest, and the highest species diversity and evenness. Our findings suggest that free grazing and lowintensity traditional grazing can be substitutive to each other; various grazing intensities from low to medium, alternating in space and/or time can be appropriate to maintain high compositional diversity.