 This paper proposes a methodology for calculating return periods and design quantiles in a multi-dimensional environment. The authors first outline a theoretical framework for the calculation of return periods using copulas and the Kindle's Tau measure. They then discuss various methods for identifying appropriate design events which are of great importance in practical applications. Finally, they use a case study involving the behavior of a damp to illustrate the proposed methodologies. This article was authored by G. Selvedori, C. de Michele and F. Durante.