Quantum chemical CI calculations with the semiempirical MO method SINDO1 are performed to study the rearrangement reactions of 1,2,6,7-octatetraen, 2,3-dimethylenebicyclo(2.2.0)hexane, 3,4-dimethylene-1,5-hexadiene and bicyclo(4.2.0)octa-1,5-diene. It is shown that the most favorable pathway of each of these six rearrangements involves the 2,3-dimethylene-1,4-cyclohexadiyl diradical as an interceptable intermediate. Two further intermediates, 1,2-divinyl-1-cyclobutene and 1,2-divinylylcyclobutane appear, but the latter with little importance. Energies and geometries of the four reactants resp. products, the three intermediates and twelve transitions states are presented. The mechanism of the rearrangements is discussed.