  In the framework of the low energy chiral Lagrangian renormalization group
equations for the couplings are investigated up to order p^6 -- as well for
SU(2)xSU(2) as for SU(3)xSU(3) chiral symmetry. Infrared attractive fixed
points for ratios of O(p^4) couplings are found, which turn out to agree with
the values determined from experiment in a surprisingly large number of cases.
Infrared attractive fixed line solutions for O(p^6) couplings in terms of
O(p^4) couplings and among O(p^6) couplings are determined.
