Results of an extensive study of the dynamical stability and dynamical behavior of envelopes of red giants are given. The region on the luminosity (L) -effective temperature (T/sub eff/) -plane within which static, thermally equilibrated envelopes are dynamically unstable is reanalyzed and is found to be more complex than has hitherto been thought. The significance of the structure of this region and its dependence on relevant physical parameters is discussed. The motion of unstable envelopes is followed by a numerical hydrodynamical code; it is found that some small amount of mass loss occurs via a shock ejection mechanism as previously suggested in the literature. It is, however, also found that this mass loss does occur repeatedly, so that a rather large amount of mass loss is expected over an evolutionary time scale.