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Taking the (2,2) strings as a starting point, we discuss the equivalentintegrable field theories and analyze their symmetry structure in 2+2dimensions from the viewpoint of string/membrane unification. Requiring theLorentz invariance and supersymmetry in the (2,2) string target space leads toan extension of the (2,2) string theory to a theory of 2+2 dimensionalsupermembranes (M-branes) propagating in a higher dimensional target space. Theorigin of the hidden target space dimensions of the M-brane is related to themaximally extended supersymmetry implied by the Lorentz covariance anddimensional reasons. The K"ahler-Chern-Simons-type action describing theself-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetricextension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher)dimensions for the M-brane target space. The proposed OSp(32|1) supersymmetricaction gives the pre-geometrical description of M-branes, which may be usefulfor a fundamental formulation of F&M theory.Comment: 12 pages, LaTeX, misprints corrected, the final version to appear in  the Modern Physics Letters

THE OSp(32|1) VERSUS OSp(8|2) SUPERSYMMETRIC M-BRANE ACTION FROM SELF-DUAL (2, 2) STRINGS