SUMMARYIn the cases A =[−1, 1] and A =[0, +∞), with w(x) = (1− x) (1+ x) , , >−1, and w(x) = x e −x , >−1, > 1 2 , respectively, in this paper we consider the corresponding Fredholm integral equations of the second kindin the spaces of continuous functions equipped with certain uniform weighted norms. Assuming the continuity of the kernel k(x, y) we use Nyström methods and prove the stability, the convergence and the well conditioning of the corresponding matrices. The last property is derived only from the continuity of the kernel and not from its special form. Error estimates and numerical tests are also included.