We compute the strong coupling constant G(B)*(B pi) (G(D)**(D pi)), w
here B* (D**) is the 0(+) P-wave b (q) over bar (c (q) over bar) stat
e, by QCD sum rules and by light-cone sum rules. The two methods give
compatible results in the limit m(Q) --> infinity, with a rather large
value of the coupling constant. We apply the results to the calculati
on of the hadronic widths of the positive parity B and D states and to
the chiral loop contribution to the ratio f(Ds)/f(D).