Evolutionary sequences of stellar models have been obtained, using the Henyey method, for stars of mass 0·8 M⊙, 0·9 M⊙ and 1·0 M⊙. The starting-point of each sequence is a star with a core of carbon and oxygen, comprising 25% of the star's mass, surrounded by helium-rich material. It is assumed that any remaining hydrogen-rich material has been ejected in the form of the planetary shell. The star contracts gravitationally until helium ignites in a shell at the composition discontinuity, and the subsequent evolution of the shell burning has been followed. No neutrino-loss processes have been considered in this investigation.