Polymethylaluminium oxide (PMAO) was prepared by reacting trimethylaluminium (AIMe3) with water in dilute dioxane solution. Several PMAO samples with different degrees of polymerizations (DP) were prepared (1 ~< DP ~< 7) either by changing reaction conditions or by fractionating the products. PMAO with DP about unity was found to be trimeric in dilute dioxane solutions but, in higher dielectric solvents, it partially dissociated into free ions. Electrical conductance measurements showed that the initially present ion-pairs were converted into another type of ion-pairs (solvent-bound ion-pairs) with a lower dissociation constant as the solution was aged. Catalytic activities of several PMAO samples in the stereoregular polymerization of propylene oxide were studied. Only a slight improvement of the stereoregular yield was observed by increasing the DP of the used catalyst. It was concluded that the methylaluminium oxide repeating units are the active species in the stereoregular polymerization and catalytic activity cannot be ascribed either to the presence of an "undetected impurity" or an "unidentified unique structure of PMAO".