Two examples illustrate the use of bivariate extremal distributions of the first type. One is the distribution of oldest ages at death for the two sexes; the other consists of the floods of the same river recorded at two stations located upstream and downstream. The first is an illustration of independence; the second, of dependence. These illustrations were chosen so as to facilitate the decision on the hypothesis of independence. We limit our consideration to the first, double exponential, extremal distribution because it can be written in a form which is parameter-free. Distribution-free tests for the hypothesis of independence and a criterion for independence of bivariate extremal distributions are given. Bivariate density curves of independent largest values are shown.