[en] Equilibrium states and domains of instability for compact, rapidly rotating stellar cores are investigated. Using a ''one-zone'' average-pressure model based on Maclaurin spheroids, regimes corresponding to degenerate dwarfs and neutron stars in the mass-angular-momentum (M,J) -plane are tested for their stability to radial and to certain nonradial modes. Both cold, catalyzed and noncatalyzed equations of state are considered. Results for upper mass limits and the onset of secular and dynamical instabilities agree reasonably well with recent work of Durisen on viscous, differentially rotating white dwarfs. Some effects of ''non-zero'' temperatures on neutrino luminosity and nondegenerate pressures are briefly considered. Scenarios for subsequent evolution of different regions in the (M,J) -plane, e.g., gravitational radiation versus viscous dissipation in triaxial configurations, binary fission, ''fizzlers,'' and collapse to black holes, are sketched