The insertions of methylidyne into PH3, H2S, HCl, NH3, H2O, and HF have been systematically studied at the MP4/6-311++G(2d,p)//MP2/6-311++G(d,p) + ZPEs and G2 levels. Each of the insertions is predicted to occur via an initially formed intermediate complex HC-XHn followed by a hydrogen-migration process. By comparison of the energetic and geometrical results of these insertions, two three-point sets of rules (rules A and rules B) are found and discussed, which are compared with those for the SiH insertions. Interestingly, the complexes HC-PH3 and HC-SH2 are found not to be the simple (loosely bound) donor-acceptor complexes as those formed in the CH insertions into other hydrides and those formed in the SiH insertions are. Their molecular and electronic structures have the following features: the short C-X bond lengths (1.723 and 1.751 Angstrom, being shorter than or comparable to the bond lengths 1.787 and 1.724 Angstrom in the corresponding products); large binding energies (47.5 and 25.8 kcal/mol, respectively); considerable charge separations; and low rotational barriers around C-X bonds. On the basis of the detailed comparison with the qualitative features of typical ylides (H2C-PH3 and H2C-SH2), HC-PH3 and HC-SH2 are considered to be similar to the ylides in nature, being "ylide-like radicals". We suggest the two radicals might be observed in some experiments since they are in deep wells in the energy surface. The calculated dipole moments and hyperfine coupling constants an reported.