  The construction of the effective Lagrangian relevant for the mesonic sector
of QCD in the large N_c limit meets with a few rather subtle problems. We
thoroughly examine these and show that, if the variables of the effective
theory are chosen suitably, the known large N_c counting rules of QCD can
unambiguously be translated into corresponding counting rules for the effective
coupling constants. As an application, we demonstrate that the Kaplan-Manohar
transformation is in conflict with these rules and is suppressed to all orders
in 1/N_c. The anomalous dimension of the axial singlet current generates an
additional complication: The corresponding external field undergoes
nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten
term, which accounts for the U(3)_R x U(3)_L anomalies in the framework of the
effective theory, contains pieces that depend on the running scale of QCD. The
effect only shows up at nonleading order in 1/N_c, but requires specific
unnatural parity contributions in the effective Lagrangian that restore
renormalization group invariance.
