Reactions of mixed phosphonium-iodonium ylides with nitriles and acetylenes allow for the synthesis of not easily accessible and novel heterocyclic compounds in a simple, one-pot, metal-free system. The results of the mechanistic investigation of the reaction of the phosphonium-iodonium ylides with acetylenes by means of spectrophotometry, EPR and NMR spectroscopy are discussed in this review. This investigation allows to account for unusual regularities of these reactions: induction time, acid catalysis, chemically induced dynamic nuclear polarization effect (CIDNP) observed in several systems, and others. The radical character of the initiation of the reaction as a result of acid catalysis of the ylides decomposition on radicals and the participation of radical intermediates in the formation of all target products have been unambiguously established. The mechanism of generation of radical pairs in CIDNP was suggested, and the role of microheterogeniety of the ylide solutions in methylene chloride was substantiated. On the basis of the study of the reaction mechanism, the conditions for the increase in the yields of new heterocyclic compounds can be optimized.