I discuss possible failures of local quark-hadron duality in the syste
m of heavy-light quark mesons. As an example, I consider a correlator
of two currents comprising heavy quark operators, and I compare the OP
E expression with the result obtained by a complete insertion of hadro
nic states. After a smearing procedure, OPE and hadronic spectral func
tions agree with each other. However, the local behaviour of the two f
unctions is different, and the difference manifests itself in a term w
hich is absent in the OPE.