Possible equilibrium states are investigated for a star consisting of a massive nondegenerate envelope surrounding a degenerate neutron core. General-relativistic stellar models are constructed that are spherically symmetric, nonrotating, devoid of magnetic fields, and in slowly evolving equilibrium states. Three interior regions are delineated, and the structure of each region is analyzed. Numerical models corresponding to red giants and supergiants are presented in which the large diffuse envelope is separated from the compact core by a thin (about 40 meters thick) nearly isothermal layer, or 'halo', where all the gravitational energy release occurs. Observable features of the models are considered along with their stability and evolution.