  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.
