Abstract: Some well-known notions in univariate statistical analysis becomes misleading in the multivariate context,and have not been correctly understood by many researchers. One example is the relationship between the expected number of events with return periods greater than or equal to T year over a N year period with the ratio N/T. Additionally,in some empirical studies,the relationship between the joint return period of a hydrological multivariate event and the corresponding return periods of its marginal distributions were found and applied. However,there lacks a detailed derivation and interpretation of this relationship. In this paper,based on the GH copula,the relationships between the bivariate return period of an event and return periods of its corresponding marginal distributions was derived theoretically,as well as the relationship between the number of occurrences of bivariate events and their primary return periods at different degrees of correlation between the two marginal variables. The theoretically derived relationships in this study were tested with drought events in Kunming identified on SPI and SRI series with 56 years of monthly precipitation and runoff data. The results suggest that the correctness of drought multivariate return period analysis could not be supported by the closeness of the primary return period of an event and the average inter-arrival time of drought events more severe than the studied event. Future researchers also need to avoid using the maximum marginal return period to approximate the primary return period of an ‘and’ event when the two marginal variables only have a weak correlation.