Astreamflow drought index was calculated by using monthly runoff from 1959 to 2009 at Makou hydrologic station in the lower reaches of the Xijiang River.The hydrologic drought duration and intensity was characterized through run theory,which were used to construct the bivariate joint distribution model in this paper.The results of drought duration and intensity joint distribution model show that: (1) There is high correlation coefficient of 0.617 between streamflow drought duration and intensity;(2) The marginal distributions of drought duration and intensity can be better represented by three-parameter Weibull distribution;(3) The Gumbel-Hougaard copula which belongs to Archimedean Copula family was selected for constructing the joint distribution model of hydrological drought duration and intensity by using goodness-of-fit test;(4) The 5 10 years return period and twenty years return period of hydrologic drought can reach to heavy drought level and extreme drought level,respectively;(5) The encounter probabilities can be provided for diagnosis and prediction of drought characteristics for the correspondence between specific drought duration and hydrological drought levels or between specific drought intensity and drought duration in the probability sense.