We introduce new concepts-a generator of degree and a diagonal section of degree for any real number . A diagonal section of degree is the one of the bivariate Archimedean copula with a generator of degree . Generators of many well-known parametric families of bivariate Archimedean copulas, including those of Clayton, Frank and Gumbel-Hougaard, are of degree . In this article, we show that each bivariate Archimedean copula with a generator of degree is uniquely determined by its diagonal section. An asymptotic representation of these copulas in terms of corresponding diagonal sections is obtained. We also provide a sufficient condition to be a diagonal section of degree . These results allow us to construct several statistical inference procedures for bivariate Archimedean copulas. Since diagonal sections of copulas are absolutely continuous, we suggest a parametric estimation procedure for bivariate Archimedean copulas based on the likelihood of a full sample from the diagonal section.