Investigations of dMe stars at Armagh have revealed a new wave phenomenon in photometric data outside stellar flares which we have attributed to coronal loop resonances. Results are based on observations of M dwarfs (strong X-ray emitting, active dMe's and inactive dM's) using a variety of techniques. Multi-band UBVRI (time res. 24s), single U-band (1s), fast infrared J,H or K (10ms), medium resolution spectroscopic (20s) and satellite-borne photometric (IUE-FES, 100ms) observations have already been analysed. Several analytic treatments useful for searches for quasi-periodicities are given in Appendices A-F. It is emphasised, however, that further analytic methods appropriate to a transient phenomenon should be applied. In an interpretation of this phenomenon, we examine what we believe might be the key related theoretical questions: What source controls the heating of quiescent coronae in active cool stars, and what is the role played by convection? For both of these the details of the physical mechanism is currently uncertain. Most probably the coronal heating is associated with subsurface turbulent motions, and controlled in some way by powerful magnetic structures and loop resonances. For example, the jostling of the loop footpoints by convection creates low-frequency variations of various modes on the magnetic field. These magneto-hydrodynamic (MHD) waves propagate from the convection zone along the loop, and a fraction of them eventually reach the corona, resonating within the length of the loop before they are dissipated. Variation of dMe star coronal emission in very large loops, or at their footpoints, may be responsible for the photometric oscillations.