The reactions of bicyclic enone (BCE, 1) with cyclopentadiene (Cp, 2), and the five-membered heterocyclic compounds (FHCs) furan 3 and N-methyl pyrrole 4 for the construction of polycyclic heterocyclic compounds have been studied at the B3LYP/6-31G* level. No reaction takes place in the absence of Lewis acid (LA) catalysts as a consequence of the high activation energy associated with these reactions. Electrophilic activation of BCE 1 by formation of a complex with the BF3 LA, 1-BF3, and solvent effects favor the reactions. However, a different reactivity is manifested by Cp 2 and FHCs 3 and 4. Thus, while the reaction of 1-BF3 with Cp 2 yields the expected exo [4+2] cycloadduct, the reactions of these FHCs yield Michael adducts. In any case, the reactions are characterized by the nucleophilic/electrophilic interaction between the most nucleophilic centers of these dienes and the most electrophilic center of complex 1-BF3. The greater ability of FHCs 3 and 4 to stabilize positive charges opposed to Cp 2 favors a stepwise mechanism with formation of a zwitterionic intermediate. Although in most stepwise Diels-Alder reactions, the subsequent ring-closure has unappreciable barriers, in these FHCs the abstraction of a proton with regeneration of the aromatic ring becomes competitive. Thermodynamic calculations suggest that the exergonic character of the formation of the Michael adducts could be the driving force for the reactions involving FHCs.