Infra-red stability of Yukawa and soft-breaking fixed points

We investigate the infra-red stability of the fixed points in the evolution of the Yukawa couplings, A-parameters and soft scalar masses in a broad cl ass of supersymmetric theories. We show that the issue of stability is esse ntially determined in all three cases by the eigenvalues of the same matrix . In a very wide range of physically interesting theories it follows that, in the asymptotically free case, the existence of stable infra-red bred poi nts for the Yukawa couplings implies stable infra-red fixed points for the A-parameters and soft scalar masses. (C) 1998 Elsevier Science B.V. All rig hts reserved.