A note on the supersymmetries of the self-dual supermembrane

In this letter we discuss the supersymmetry issue of the self-dual supermembranes in (8+1) and (4+1)-dimensions. We find that all genuine solutions of the (8+1)-dimensional supermembrane, based on the exceptional group G2, preserve one of the sixteen supersymmetries while all solutions in (4+1)-dimensions preserve eight of them.