A subclass of Levy-stable distributions, i.e., symmetric /spl alpha/-stable distributions (S/spl alpha/S), is applied to mutation operators of evolutionary strategies (1+1)ES/sub /spl alpha// and (1+/spl lambda/)ES/sub /spl alpha//. The local convergence rate of algorithms is considered. Moreover, some conditions are established under which evolutionary algorithms with mutation based on distributions with heavy tails generally have better local as well as global convergence. In order to justify the theoretical deliberations, some illustrative numerical simulations are presented.