  Exact instanton solutions to $D=11$ spherical supermembranes moving in flat
target spacetime backgrounds are construted. Our starting point is Super
Yang-Mills theories, based on the infinite dimensional $SU(\infty)$ group,
dimensionally reduced to one time dimension. In this fashion the super-Toda
molecule equation is recovered preserving only one supersymmetry out of the
$N=16$ that one would have obtained otherwise. It is conjectured that the
expected critical target spacetime dimensions for the (super) membrane,
($D=11$) $D=27$ is closely related to that of the $noncritical$ (super)
$W_{\infty}$ strings. A BRST analysis of these symmetries should yield
information about the quantum consistency of the ($D=11$) $D=27$ dimensional
(super) membrane. Comments on the role that Skyrmions might play in the two
types of Spinning- Membrane actions construted so far is presented at the
conclusion. Finally, the importance that integrability on light-lines in
complex superspaces has in other types of solutions is emphasized.
