Based on a linear and non-linear study of radial pulsations in the envelopes of classical novae (Schenker, 1999), I discuss the results both from the point of view of pulsation theory as well as their consequences for current nova models. Starting from initially static envelope structures at various stages during the decline of a nova outburst, strong ‘running-wave’ instabilities have been found that rapidly grow into shocks. Improved analytical concepts give a new direction to the interpretation of such highly non-adiabatic radial pulsations. For direct observational confirmation, a search for short period variability in the UV and soft X-ray is suggested during the very late decline phase. Speculative consequences for mass-loss scenarios in novae due to these instabilities will need some more work in the future.