By means of Al-27, H-1, O-17 and C-13 NMR spectroscopy the structure of the methylaluminoxane (MAO) cocatalyst of Kaminsky-Sinn catalysts was investigated. We have found that the Al-27 NMR resonance line of MAO is extremely broad at room temperature (delta approximate to 60, Delta omega(1/2) 50 +/- 10 kHz). At elevated temperatures (40-120 degrees C) MAO exhibits an Al-27 resonance at delta 110 +/- 10, Delta omega(1/2) 15 - 10 kHz, that is, within the range reported for the aluminoxane clusters [(t-Bu)Al(mu(3)-O)](6) and [t-Bu)Al(mu(3)-O)](9) with cage structures. The Al-27 resonance at delta 149-153, usually attributed to MAO, belongs to AlMe3 present in MAO samples. The O-17 NMR resonance of MAO at 50 degrees C (delta 67, Delta omega(1/2) 1.7 kHz) is within the range typical for three-coordinate oxo ligands, but it can be attributed only to a minor part of MAO oligomers. It was shown that the intensity of Al-27 and O-17 NMR resonances of MAO increases with increasing temperature, whereas the width of both resonances is almost constant. The results obtained lead to the conclusion that at ambient conditions MAO forms oligomers (MeAlO)(n) with cage structure and MeAlO3 environment. Upon increasing the temperature these oligomers reversibly break into smaller MAO units. Based on the Al-27 NMR data the average radius (R) of MAO oligomers is approximately 5.1 +/- 0.3 Angstrom at 120 degrees C. This radius corresponds to (MeAlO)(n) species with 9 < n < 14. At ambient conditions the predominant part of MAO forms oligomers with R = 7 +/- 0.5 Angstrom and 20 < n < 30.