The potential energy surfaces of the ground state (S-0) and triplet pi pi* (T-1) state for the cycloaddition of acrolein to ethylene have been mapped with ab initio CASSCF calculations and the 6-31G* basis set. The results indicate that transition states on both the triplet and ground-state surfaces play a part in controlling product selectivity, in accord with the experimental results of Weedon and co-workers. The first part of the reaction involves attack of the alkene by either the alpha- or beta-carbon of the triplet cis or trans alpha,beta-enone leading to many different anti and gauche conformations of a triplet biradical intermediate, which then undergoes intersystem crossing to the ground-state surface. The second part of the reaction is controlled by the groundstate surface topology. Ring-closure to products competes with reversion to reactants; anti birodicals have a tendency to dissociate while gauche biradicals favor cyclobutane formation. The addition of the n pi* states of acrolein to ethylene has higher barriers than found for the 3(pi pi*) state. alpha-Attack is strongly disfavored as it involves decoupling electrons, but the barriers for beta-attack leading to 1,6-birdicals lie only a few kilocalories per mole higher in energy than those on the (3)(pi pi*) surface, suggesting that in more constrained enone systems the n pi* states may play a role. Two (1)(n pi*)/(3)(n pi*)/(3)(pi pi*) crossing regions exist, the first in acrolein itself and the second in the 1,6-biradical region. In the parent system, the biradical crossing points lie some 16 kcal/mol above the n pi* minima, such that fast intersystem crossing or internal conversion is more likely to occur before the transition state region. However, in more constrained systems, the reaction could proceed on the n pi* states into the biradical region, followed by decay through the four-level degenerate crossing points.