Two DFT methods are used to study the stability, singlet-triplet splitting, and geometry of all didehydrogenated quinolines and isoquinolines in their lowest lying singlet and triplet states. Here, the relative stability within an isomeric series is differentiated from the biradical stabilization energy, which pertains to the propensity for radical abstraction reactions. Analysis of relative stability orders for these hetarynes points to the influence of the basic hetaryne type (ortho, meta, peri, para, and other), the effects of bond alternation in the bicycle, and the position of the ring nitrogen atom with respect to the nearest radical center. Singlet hetaryne stability tends to follow the order ortho > meta > (para and peri) and the reverse order for the triplet species. Among ortho-hetarynes, the singlet state is stabilized, and the triplet state destabilized when the hetaryne bond is shorter, and vice versa. The effects of the nitrogen atom on the relative stability depend upon (a) the hetaryne spin state, (b) whether the nitrogen is adjacent to or one atom removed from a radical center, and (c) the distance between the heteroatom and the nearest radical center for hetarynes with more widely separated radical centers. The singlet-triplet splitting is, in most cases, more dependent upon singlet stability than triplet stability. The biradical stabilization energy does not, in general, correlate with relative stability but furnishes predictions concerning capacity for reactions like hydrogen atom abstraction. Geometries of the singlet hetarynes (notably the ortho- and meta-hetarynes) present greater departures from the parent hetarene structure than do the triplet geometries.