  Taking the N=2 strings as the starting point, we discuss the equivalent
self-dual field theories and analyse their symmetry structure in 2+2
dimensions. Restoring the full `Lorentz' invariance in the target space
necessarily leads to an extension of the N=2 string theory to a theory of 2+2
dimensional supermembranes propagating in 2+10 dimensional target space. The
supermembrane requires maximal conformal supersymmetry in 2+2 dimensions, in
the way advocated by Siegel. The corresponding self-dual N=4 Yang-Mills theory
and the self-dual N=8 (gauged) supergravity in 2+2 dimensions thus appear to be
naturally associated to the membrane theory, not a string. Since the same
theory of membranes seems to represent the M-theory which is apparently
underlying the all known N=1 string theories, the N=2 strings now appear on
equal footing with the other string models as particular limits of the unique
fundamental theory. Unlike the standard 10-dimensional superstrings, the N=2
strings seem to be much closer to a membrane description of F&M theory.
