Plants minimize fitness losses through grazing by three fundamental strategies: tolerance, avoidance and escape. Annual species have been traditionally assumed to escape grazing through their short life cycle and seed dormancy; however, their grazing response strategies remain almost unexplored. How traits and their coordination affect species' grazing responses, and whether the generalized grazing model, which posits convergent filtering by grazing and drought, is applicable to this ecologically and economically important species group thus remain unclear. We used a trait-based approach to evaluate grazing response strategies of winter annuals from the Middle East. Across 23 species, we examined the coordination of 16 traits hypothesized to be relevant for grazing responses, and linked them to species' fecundity responses, as proxy for fitness responses, to simulated grazing in controlled conditions, to species' abundance responses to grazing in the field and to species' distribution along a large-scale rainfall gradient. Winter annuals exhibited both grazing escape and to a lesser extent tolerance indicated by (a) independent coordination of escape and tolerance traits, and (b) maintenance of higher fecundity in species with more pronounced escape or tolerance traits under simulated grazing. In the natural habitat, species with a more pronounced escape but not tolerance strategy maintained higher abundance under grazing in dry habitats, indicating convergent favouring of escape by both grazing and drought. However, this finding at the local scale was not mirrored by a strategy shift along a large-scale rainfall gradient. Synthesis. The convergent favouring of escape traits by grazing and drought in annuals is consistent with the generalized grazing model. This model, which has been developed for perennials based on the avoidance strategy, can thus be extended to annuals based on escape, a finding that should facilitate projecting consequences of global change in drylands dominated by annuals. © 2021 The Authors. Journal of Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society