The time-dependent theory of wave packet dynamics accompanying the excitation and decay in the molecular Auger process is reviewed and applied to the resonant Auger spectrum of HF. When the core-excitation is performed by an energetically non-selective source (`broad-band' excitation), many intermediate states are populated during the excitation process and their decay gives many interplaying contributions within the same energy region. To interpret the spectrum we have carried out a detailed theoretical study of all the decaying and final electronic states involved. In order to restrict the number of participating decaying states, narrow-band excitation has to be performed, so that only one intermediate decaying state is populated. We have studied in detail one particular transition between purely repulsive potential curves, where we show the effects introduced by the energetically selective excitation. By detuning the excitation energy off the resonance, very prominent interference patterns can be found. These explain the quenching of the so-called `atomic lines' and the surprising new features which appear in the case of small detuning towards higher excitation energies. The effects discussed are shown to be of a general nature. The description in the time-dependent picture allows for a novel and deeper understanding of the underlying mechanisms of these effects since the physically relevant quantities can be traced on the real time scale of the process.