Cyclobutadiene and benzocyclobutenes fused to o- and p-quinone have been studied by computational methods. Geometries were optimized at the B3LYP/6-31G* level, and absolute NMR shielding values were calculated using the GIAO method with the HF/6-31G* basis set. NICS values of the compounds 8b,c and 9b,c indicate strong antiaromatic character for cyclobutadiene units. However, 8a and 9a show negative NICS values where the quinodal system reduces the antiaromaticity significantly by forcing these systems to possess a dimethylene-like structure. The calculated C-13 NMR chemical shifts of 6-9 and parent systems are in very good agreement with literature values.