[en] We propose a new method for the computation of the high energy limit of the total cross section in spontaneously broken gauge theories. It is based on an evolution equation for effective couplings in dependence on the gauge boson mass. We apply this method to weak interactions in the leading logarithm approximation. Perturbation theory becomes invalid at very high energies since one of the couplings becomes strong. The obtained total cross sections obey Froissart's bound, in contrast to previous results not using the evolution equation. (orig.)