Atomic-level understanding of the nature of the electronically excited states in ligand-stabilized metal nanoclusters (NCs) is a prerequisite for the design of new NCs with desired properties. In this study, we investigate the emission dynamics of a Ag-DNA complex using the fluorescence up-conversion technique. We show that most of the relaxation from the Franck-Condon state to the emissive state takes place in less than 100 fs, in spite of a relatively large Stokes shift of 4500 cm^-1. This relaxation is much faster than typical solvent/DNA relaxation rates. A further small relaxation occurs with time constants ranging from a few to hundreds of picoseconds. We also calculate the Stokes shift for model complexes of a small three-atom Ag₃ ⁺ cluster with cytosine and guanine. The results of our calculations show that a substantial geometry change of the Ag₃ ⁺ cluster is observed in the S1 state of both complexes, which results in Stokes shifts comparable with the experimental value. We conclude that the Stokes shift in the Ag-DNA complex arises mostly due to the change in the geometry of the Ag cluster in the excited state rather than to the solvent/DNA reorganization. Also, a different structure of the Ag-DNA complex ("dark cluster"), the excited state of which decays in 200 fs, is observed. The nature of this ultrafast deactivation is unclear, which requires further investigations.