Drought is a natural disaster that threats the all creatures because of its complexity of its nature and difficulties in its prediction to its effects on nature, economy, social life and water existence. The aim of the study is to construct univariate and bivariate return periods for hydrological droughts characteristics which are drought severity and drought duration in 6 month scale, using mean monthly streamflow records of 4 stations in Kizilirmak Basin of Türkiye, Streamflow Drought Index (SDI) and copula functions. From calculated SDI values and Yevjevich’s Run Theory drought severity and drought duration are calculated. Non-parametric rank correlation coefficient is used to measure dependence between severity and duration. Six marginal distributions are used to model the marginal distributions of duration and severity. Using best fit marginal distributions, for constructing univariate return periods in 10, 20, 50, 100, 200, 500 years, and bivariate return periods considering the TDS (and) and T′DS (or) cases; Gaussian, Student’s t, Clayton, Gumbel, Frank, Joe, BB1, BB6, BB7 and BB8 copulas are utilized. The best copulas have been analyzed by tail dependence and by goodness of fit tests. Results have shown that drought severity and duration series are correlated with each other highly. Mostly, Lognormal distribution has modelled the drought duration and severity series as best. Gumbel and BB1 copulas have shown better results for modelling the return periods. The findings of the study will help to design of hydraulic structures and decision making in water resources management.