Abstract: Bivariate return periods of floods, with peak flood discharge x and flood volume y as variables, are important to calculation and evaluation of flood control in hydraulic engineering. For a flood event, calculation of its return periods much depends on its components and how to match the demands. This paper discusses and calculates four types of return periods using the Copula function theories ? univariate return period N1, OR-event return period N2, AND-event return period N3, and matching return period N4 ? focusing on the demonstration of N4. And the four return periods are compared in a case study of the Mabian hydrological station of the Mabian River, a branch of the Minjiang River. The results show that for a given set (x0, y0) of the bivariate variables, the values of these periods are quite different. When both x0 and y0 are large or small, they follow a decreasing order of N3> N4> N1> N2; when x0 is large and y0 is small or y0 large and x0 small, N4 could become possibly much larger than N3 or even smaller than N1. Thus, attention should be paid to the special properties of the Copula functions and we recommend the use of bivariate matching values N4 in flood control calculations.