Perennial grasses are the key to the economic and environmental sustainability of pastures for livestock grazing in south-eastern Australia. Mortality of perennial grasses can occur during drought periods and there is anecdotal evidence of differences in drought resistance among species, but information on the basic ecophysiological responses of these species to drought is lacking. An experiment was conducted to determine the responses of 7 native and 3 introduced perennial grass species to continuous drought. Leaf survival during severe drought varied among the species nearly 4-fold, from 11 to 40 days, and was considered a measure of their overall drought resistance. All of the species had good dehydration tolerance, so the differences in drought resistance were related more to their dehydration avoidance traits, specifically to the amount of water available to the plant at the point where plant transpiration became minimal. The native species had both the longest and shortest leaf survival periods, with the introduced species ranking intermediate. Species exhibited various morphological traits that contributed to dehydration avoidance during severe drought, including leaf folding or rolling, rapid leaf shedding, and large amounts of cuticular wax. The results are discussed in terms of their implications for perennial grass persistence in south-eastern and in south-western Australia.