Present stellar evolution codes predict that stars with He-core masses above approximately 2 M⊙, corresponding to main sequence masses of at least 8 M⊙ burn carbon non-violently. After hydrostatic core carbon burning all those stars contain O-Ne-Mg cores but their further evolution is strongly dependent on the stellar entropy and thus on the main sequence and the core mass. If the He-core mass is below 3 M⊙ the O-Ne-Mg core grows due to carbon-burning in a shell and the crucial question is, whether or not it grows beyond the critical mass for Neignition (≅1.37 M⊙). Stars with He-cores less massive than about 2.4 M⊙ will never ignite Ne, but due to electron-captures, mainly on Ne and Mg, their cores will contract until O-burning begins. Since the matter of the O-Ne-Mg core is weakly degenerate O-burning propagates as a (subsonic) deflagration front and incinerates a certain fraction of the core into a nuclear statistical equilibrium (NSE) composition of iron-group elements (Nomoto, 1984). If, on the other hand, the mass of the O-Ne-Mg core is slightly larger than 1.37 M⊙ Ne and O burn in a shell from about 0.6 M⊙ to 1.4 M⊙, but again the outcome is a NSE-composition (Wilson et al., 1985). In both cases the core-mass finally exceeds the Chandrasekhar limit because electron captures on free protons and heavy nuclei lower the electron concentration and consequently also the effective Chandrasekhar mass. The cores, therefore, continue to contract and finally collapse to neutron star densities with iron-core masses between 0.7 and 1.4 M⊙.