This paper deals with the problem of estimating the tail of a bivariate distribution function. To this end we develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. We introduce a new parameter that describes the nature of the tail dependence and we provide a way to estimate it. We construct a two-dimensional tail estimator and study its asymptotic properties. We also present real data examples which illustrate our theoretical results.