Methanol conversion reaction was carried out in contact with a poorly crystalline -alumina pre-irradiated with different doses of -rays. The reaction was conducted at 140–440°C using a flow technique under atmospheric pressure. The results obtained revealed that -irradiation of Al2O3 resulted in drastic modifications of its activity and selectivity in methanol conversion reaction. The dose of 15 Mrad was sufficient to suppress completely the formation of dimethyl ether (DME) and stimulated the formation of methane, which started at 200°C instead of 300°C in the case of the unirradiated alumina specimen. However, the rate of CH4 formation was found to decrease as a function of the dose employed. When the dose reached 140 Mrad, DME was reproduced with a rate comparable to that measured for the unirradiated catalyst sample. These results permitted us to conclude that DME is produced on the weak acidic sites (Brönsted acidity of Al2O3) and is not necessarily an intermediate compound for methane formation that takes place directly from methanol on strong acidic sites (Lewis acidity). The doses of 15–75 Mrad expelled completely the Brönsted acidic sites from Al2O3 surface, and the doses above this limit brought about a transformation of Lewis acidic sites into Brönsted acidity that is responsible for dimethyl ether formation. This transformation occurs by the action of liberated water from the dehydration of methyl alcohol.