  We report on some recent progress made in understanding weak matrix elements
of mesons in the context of the next-to-leading order of the large-Nc
approximation to QCD. Specifically, we first use the example of the weak
contributions to the pi^+ - pi^0 mass difference to exhibit how a systematic
matching can be achieved analytically between short distances and long
distances within our large-Nc framework. We are then also able to compute
matrix elements of the operator Q_7, as they turn out to depend on the same QCD
correlator as the previous pion mass difference. As a final example we
determine the chiral counterterms governing the pseudoscalar decay into a
lepton pair, where we briefly comment also on the special case K_L -> mu^+
mu^-.
