The reaction paths of [2+2] cycloaddition of the X=C=Y cumulenes were modeled at the MP2/aug-cc-pVDZ level. Cycloadditions of allene and CO2, CS2, or OCS lead in part to the same four-membered products as dimerizations of either ketene or thioketene or addition of ketene and thioketene, respectively. All the reactions studied are concerted and mostly asynchronous. The majority of the allene cycloadditions studied are endoergic and proceed with much higher activation barriers than do the alternative (thio)ketene additions. In comparison with the energy of the substrates, the four-membered cycles incorporating S-atoms are stabilized more than the analogous structures with O-atoms built into the rings. There are also some products that are thermodynamically disfavored, yet seem to be obtainable thanks to a relatively low barrier of the reaction. The AIM analysis of the electron density distribution in the transition state structures allowed distinguishing pericyclic from pseudopericyclic and nonplanar-pseudopericyclic types of reaction.