The bond dissociation energies of CH4, C2H2, and their fragments are investigated using basis set extrapolations and high levels of correlation. The computed bond dissociation energies (D-e) are accurate to within 0.2 kcal/mol. The agreement with the experimental (D-O) values is excellent if we assume that the zero-point energy of C2H is 9.18 kcal/mol. The effect of core (carbon Is) correlation on the bond dissociation energies of C-H bonds is shown to vary from 0.2 to 0.7 kcal/mol and that for C-C bonds it varies from 0.4 to 2.2 kcal/mol.