Experimental and ab initio molecular orbital techniques are developed for study of aluminum species with large quadrupole coupling constants to test structural models for methylaluminoxanes (MAO). The techniques are applied to nitrogen- and oxygen-containing complexes of aluminum and to solid MAO isolated from active commercial MAO preparations. (Aminato)- and (propanolato)aluminum clusters with 3-, 4-, and 6-coordinate aluminum sites are studied with three Al-27 NMR techniques optimized for large Al quadrupole coupling constants: field-swept, frequency-stepped, and high-field MAS NMR. Four-membered (aminato)aluminum complexes with AlN4 coordination yield slightly smaller C-q values than similar AlN2C2 Sites: 12.2 vs 15.8 MHz. Planar 3-coordinate AlN2C sites have the largest C-q values, 37 MHz. In all cases, molecular orbital calculations of the electric field gradient tensors yields C-q and eta values that match with experiment, even for a large hexameric (aminato) aluminum cage. A D-3d symmetry hexaaluminum oxane cluster, postulated as a model for MAO, yields a calculated C-q of -23.7 MHz, eta = 0.7474, and predicts a spectrum that is too broad to match the field-swept NMR of methylaluminoxane, which shows at least three sites, all with C-q values greater than 15 MHz but less than 21 MHz. Thus, the proposed hexaaluminum cluster, with its strained four-membered rings, is not a major component of MAO. However, calculations for dimers of the cage complex, either edge-bridged or face-bridged, show a much closer match to experiment. Also, MAO preparations differ, with a gel form of MAO having significantly larger Al-27 C-q values than a nongel form, a conclusion reached on the basis of Al-27 NMR line widths in field-swept NMR spectra acquired from 13 to 24 T.