  We study the evolution of $R$-parity-violating (RPV) couplings in the minimum
supersymmetric standard model, between the electroweak and grand unification
scales, assuming a family hierarchy for these coupling strengths. Particular
attention is given to solutions where both the $R$-conserving and $R$-violating
top quark Yukawa couplings simultaneously approach infrared fixed points; these
we analyse both algebraically and with numerical solutions of the evolution
equations at one-loop level. We identify constraints on these couplings at the
GUT scale, arising from lower limits on the top quark mass. We show that fixed
points offer a new source of bounds on RPV couplings at the electroweak scale.
We derive evolution equations for the CKM matrix, and show that RPV couplings
affect the scaling of the unitarity triangle. The fixed-point behaviour is
compatible with all present experimental constraints. However, fixed-point
values of RPV top-quark couplings would require the corresponding sleptons or
squarks to have mass $\agt m_t$ to suppress strong new top decays to
sparticles.
