The [2 + 2] cycloadditions of cyclopentyne and benzyne to ethylene are explored at the B3LYP and CASSCF levels, supplemented by CCSD(T) and CAS-MP2 calculations at the stationary points. The biradical path in the benzyne system is computed to be about 4.1 kcal/mol lower than the concerted path, consistent with the experimentally observed loss of original stereochemistry in this cycloaddition. However, computations fail to confirm the 99% stereoretention in the corresponding reaction of cyclopentyne. The concerted and biradical paths in the latter reaction are found to involve nearly isoenergetic barriers, thus predicting only about 75% stereoretention. More sophisticated theoretical methods seem to be needed to resolve the issue in the cyclopentyne system.