HMO correlation diagrams for some competing 1,2-and 1,4-cycloaddition reactions have been made to elucidate the reaction mechanism. The main conclusions obtained from this study are as follows. 1) The crossing between the highest occupied molecular orbital and the lowest unoccupied molecular orbital was not observed, which indicates that the reaction proceeds thermally, in agreement with the experimental results. 2) From the consideration of the energy barrier in the process of the energy transformation going from reactants to product, the two-step mechanism via a diradical intermediate is preferred over the concerted one. 3) The existance of diradical intermediates can account for the observed product distributions.