An analytical investigation of Alfv¿n resonances is presented for the cases when energy is dissipated by (1) resistivity (&eegr;) within the body of the plasma, and (2) finite Pedersen conductivity (&Sgr;p) within the ionospheric boundaries. Universal functions for both solutions are compared, and we find that the structure and phase motion of the resonant fields is fairly insensitive to the details of dissipation. We also identify a curious property of resonances: the spatially integrated (but not time-averaged) dissipation rate is independent of time for whichever dissipation process we consider. It appears that resonances have a remarkably robust structure. ¿ American Geophysical Union 1996