Schwarzschild and Härm (1970, hereafter abbreviated SH) have suggested that the presence of Cepheids in globular clusters can be explained by the occurrence of ‘flashes’ in the thermally unstable helium-burning shells of post-horizontal-branch, or ‘asymptotic-branch’ stars. These flashes in the deep interior of the star produce large changes in the energy flux at the base of the envelope, which in turn cause the position of the model in the Mbol — logTe diagram to move. For most values of the total stellar mass and envelope composition studied by SH, the models simply moved up and down the asymptotic branch in response to a helium shell flash. However in a few cases, characterized by low total mass and a relatively high value of the envelope helium abundance, the models left the asymptotic branch and described loops extending into the region of pulsational instability. The Cepheids of Population II were thus tentatively identified by SH as asymptotic-branch stars that had recently undergone a helium shell flash and whose tracks were as a result describing a loop extending into the instability strip.