A critical study has been made of Hafner's new heptalene and pentalene derivatives I and II. Conventional valence-bond, molecular-orbital and free-electron approximations have been used. All agree that I should be genuinely aromatic, and II should not be. The valence-bond method suggests that II should be pseudo-aromatic, the other methods suggest that it should possess cyclo-olefinic character. All methods confirm the very long wavelength absorption of I, but the agreement in the case of II is less satisfactory. Charge distributions, bond orders and lengths are calculated by the molecular-orbital method, and compared with heptalene, pentalene, azulene and acenaphthylene. The relevance of the aromatic sextet rule is pointed out in discussing charge distribution in these odd-numbered ring compounds. Localization energies are also calculated, and are used to predict the positions of greatest reactivity for electrophilic, nucleophilic and radical reactions.