Degenerate U− and V−statistics have asymptotic distributions that are given by an infinite weighted sum of χ2 random variables, whose weights are the eigenvalues of an integral operator whose solution is in general very difficult. We provide a new computational approximation of the eigenvalues and of the asymptotic distribution. As an illustration, we show that our algorithm is able to recover the tabulated asymptotic distribution of the Cramér-von Mises statistic.