Аннотация:The model of a red giant star with a neutron core proposed by Thorne and Zytkow (1975) is analyzed theoretically with respect to temporal evolution. The lifetime and accretion rate of the envelope surrounding neutron core are computed on the basis of boundary conditions. It is found that the strong neutrino emission which develops as the neutron core moves to deeper layers of the envelope implies temperatures greater than the upper limit identified by Thorne and Zytkow in their original formulation of the model. It is also found that allowing for the release of gravitational energy in the massive envelope results in the expansion of the possible outflow of material at a rate of about 0.00001 solar mass per year. It is concluded that only stars with hot neutron cores (greater than 10 to the 10th K) and a high neutrino luminosity could possibly exist, and their lifetime before collapse would be about 100 years.