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 class of supersymmetric theories. We show that the issue of stability is essentially 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 fixed points for the Yukawa couplings implies stable infra-red fixed points for the $A$-parameters and soft scalar masses.